The Similarity Transform Song

(to the tune of “If You’re Happy and You Know It“)

Note: This song describes what to do for a similarity transformation to find the eigenvalues of a matrix A. A similarity transform changes the matrix but does not alter its eigenvalues. Ideally, if you could find a similar matrix that was diagonal, you could pick the eigenvalues right off the diagonal. A similarity transform is of this form: B = T^{-1} A T, where T is the similarity transform matrix, and B is the matrix that is similar to A.

If your matrix has distinct eigenvalues,
It is very much apparent what to use:
Choose nonsingular for T,
and get a diagonal B,
If your matrix has distinct eigenvalues.

If you have a real symmetric matrix A,
Choose orthogonal for T: it’s the best way!
Because, after all
B is real diagonal
If you have a real symmetric matrix A.

If it’s complex and Hermitian, never fear!
The solution to your problem is quite clear:
Use a unitary T,
to get a real diagonal B
If it’s complex and Hermitian, never fear!

If your matrix A is normal as can be,
Take the following advice from me:
If your T is unitary
B’s diagonal (how scary!)
If your matrix A is normal as can be.

If A is chosen arbitrarily,
and you find a T that’s unitary,
Then B has the form of Schur
(that’s upper triangular)
If A is chosen arbitrarily.

If A is once again arbitrary,
Then you choose “nonsingular” for T,
B is almost diagonal,
(that’s Jordan form, y’all!)
If A is once again arbitrary.

“The Similarity Transform Song” Copyright (c) 2000 Rebecca Hartman-Baker.(from

Found this while surfing. Was really funny and interesting.

10 Things That Will Change The Way We Live

Forbes website has a list of ten things that we might see in our lifetimes — some are sci-fi and the rest are more plausible — sounds interesting. Read on:

Fuel Cells

In fuel cells, the energy of a reaction between a fuel, such as liquid hydrogen, and an oxidant, such as liquid oxygen, is converted into electrical energy. Fuel cells will change the global economy, and not just because they will be as big a development in motoring as the internal-combustion engine was. They will also be used as cell-phone batteries and power generators, among other things. And they will eliminate the problem of what to do with used batteries: Theoretically, fuel cells are renewable forever.

Gene Therapy

Although the FDA has not approved any human gene therapy for sale, the potential for using it to correct defective genes responsible for disease development is enormous. Gene therapy works by inserting genes into cell tissue, essentially replacing a defective gene with one that works. So far, researchers have been exploring how gene therapy could be used to combat or eradicate diseases caused by single-gene defects, such as cystic fibrosis, hemophilia, muscular dystrophy and sickle cell anemia. With time, however, it is hoped that it will not only revolutionize the treatment of all disease but will also be able to prevent hereditary diseases, such as Down syndrome and heart disease.


Whether people know it or not, haptics has been subtly making inroads into everyday life in the form of vibrating phones, gaming controllers and force-feedback control knobs in cars (BMW’s iDrive system uses the technology). But the science of haptics has the potential to do much more. Products, such as the CyberForce “whole-hand force feedback system” from Immersion Corporation and SenseAble Technologies, let users interact physically with virtual objects. For instance, by using a sensor-equipped glove and a force-reflecting exoskeleton, you could literally feel the shape, texture and weight of an onscreen 3-D object. Such devices are used now for virtual modeling, medicine and the military, but as costs decrease, haptic interfaces could become valuable communication tools. Using haptics technology, people will be able to shake hands virtually over the Internet, and doctors will have the ability to remotely diagnose and operate on patients.


Internet2, or UCAID (University Corporation for Advanced Internet Development), is the next-generation Internet. It is a nonprofit consortium developed by many of the leading universities in the U.S., as well as by companies such as Cisco, Intel and Comcast, in 1996, to deliver video and data at much faster speeds than are possible over the public Internet. The reason is that it is connected to the Abilene national backbone–provided by Qwest Communications–by regional fiber networks, which will soon have a capacity of 10 gigabits per second through the use of optical-networking technologies. This will allow for faster downloads of more complex packets of data and facilitate activities such as peer-to-peer applications, high-definition videoconferencing and, yes, gaming.


What’s the most precious liquid on earth? If you said oil, you’re wrong. It’s water. Even though more than 70% of the earth’s surface is covered in H20, many parts of the world suffer from a persistent and crippling shortage of potable drinking water. LifeStraw hopes to change all that. The 10-inch-long, 1-inch-in-diameter device is made by Vestergaard Frandsen S.A. of Lausanne, Switzerland, out of a patented resin that kills bacteria on contact. Its filters remove bacteria, such as salmonella and staphylococcus, from surface water in rivers and lakes. Reusable and, at $3 to $4 each, affordable, it has the potential to not only reduce the outbreak of disease but also to improve living standards and sanitation in many of the world’s poorest regions.


MRAM, or Magnetoresistive Random Access Memory, could change the way we work. Researchers at IBM have shown that MRAM can be six times faster than the current industry-standard memory, dynamic RAM (DRAM). It is almost as fast as static RAM (SRAM) and is much faster and suffers less degradation over time than Flash memory. Unlike these technologies, MRAM uses magnetism instead of electrical charges to store data. As a result, it is lower in density and in cost. In December 2005, Sony engineers verified operation of a spin-torque-transfer MRAM in the lab with data-write speeds of two nanoseconds. If adopted as a universal standard, MRAM could have significant military communications applications.

$100 Laptop

If we are to accept that the world economy is now fully dependent upon the information economy, then it stands to reason that those people who are left out of the global information network are doomed to an endless cycle of poverty. The Massachusetts Institute of Technology Media Lab has designed a fully functional laptop computer that can be sold for $100, so that children in poor or developing nations can get access to the Internet. To keep costs down, the laptop will use a $35 dual-mode display (the kind found on cheap DVD players), a 500-megahertz processor, a slimmed-down operating system and will have only one gigabyte of storage. Users will be able to plug it into a wall outlet or charge it by a crank-driven battery, and it will connect to the Internet via a wireless card. To be sure, these laptops are not going to be playing Quake 4 anytime soon, but they could give disadvantaged kids a shot at taking part in the digital community. MIT hopes to have a working prototype by November 2005 and production units shipping to government education ministries by the end of 2006.

$200 Barrel Of Oil

It’s not an invention, but it will have a dramatic effect on the way everyone lives. Although the predictions range from terrifying to calming, all experts agree that a dramatic rise in the cost of fossil fuel would have a devastating impact not only on the global economy but on global society as well.


Voice-over-Internet Protocol lets people make telephone calls over the Internet or any other IP-based network. Because the voice data flows over a general-purpose packet-switched network, instead of dedicated, circuit-switched voice transmission lines, the cost of making telephone calls for both business and residential users is much less than with traditional telcos. The reason it is so cheap is that the high-speed Internet providers essentially bundle VoIP free with Internet access. Another advantage is that it is mobile: All one needs is an Internet connection to make a phone call from anywhere. But there are a few drawbacks–although these are being smoothed over–such as quality and reliability.


WiMAX stands for Worldwide Interoperability for Microwave Access, which is a long-range, standard-based wireless technology that will effectively allow people to access their phones, computers and the Internet from virtually anywhere. No more need to wait for the cable or phone company to install the “last mile” of pipe to your home. The IEEE 802.16 broadband wireless access standard provides up to 31 miles of linear service area range and allows for connectivity between users without a direct line of sight. This is significant for several reasons: First, it will increase the ease and frequency with which people make wireless connections for work or leisure; second, it will have enormous potential applications in underdeveloped countries–as well as rural areas of the First World–which lack adequate communications infrastructure; and third, no more messy wires.

Full article at (with images):

read more | digg story

4-1 Series roundup: The Emperor strikes back, the crown prince graduates

The ODI series in Pakistan has been quite wonderful for India. It was a kind of turnaround after the Karachi result and more importantly a revenge well-exacted, for the loss in the ODI series at home last year, particularly since we won four matches on the trot. If there was one thing that killed Pakistan in this series, it was their too-abysmal-for-words fielding. It was hardly even club class, save for a few of the cricketers. Apart from misfields and overthrows, the worst part was that they hardly collected even the balls they fielded properly. Woolmer’s got some work on his hands!

As for India, the Emperor (read Sachin) struck back, both with bat and ball just to prove, if at all he needed to, as to who’s still the boss. More importantly, Yuvaraj really matured as a batsman, played with an unbelievable head on his shoulders. The bowlers did their job and Dhoni, has worked real magic. The real test for Dhoni would start in the near future, when teams, having realised his potential and the danger he holds, start working on him. Interesting cricket lies ahead.

As for Dravid, he’s wonderfully jelled; he’s contributed as a batsman quite well but more importantly captained quite astutely. I’d still like to see him defend totals better, considering we kinda faltered in Game 1.

Overall, it’s been a memorable series, with a lot of positives. Sreesanth, RP Singh are all proving to be good material, and we’re surely having a problem of plenty in the pace department ahead of the World Cup. We need to pull up our socks a bit in the test matches as well, and we’re well on our way to becoming a very very good team. Kaif must soon get back into form; there’s no reason to hold Ganguly back, if Kaif is performing so badly.
Postscript: I think we’ve shot up on ICC ODI rankings. I guess we’re 2. Good job. Good form.

Seven years down memory lane

It’s the 17th of February today, seven years past 17-2-1999, when we did have our last day in DAV Boys Senior Secondary School, Gopalapuram. Have several wonderful memories of this beautiful phase of life, from a school where I studied for twelve long years. Like several of my classmates, I owe a whole lot o DAV, for what I am. We had mostly great teachers right till the very end (when problems did begin to crop up) and always a great batch of students. From being very studious to extremely mischievous, we all had our great times in DAV.

On 17th Feb, we had our farewell havan, as well as several farewell speeches, a victory lap around the school, capped by a treat at Pizza corner! There are possibly people whom I’ve not met ever since, and those whom I keep in touch with till this very day. The new bluwiki home at is indeed helping.

Schooling is always a treasured memory from childhood. I owe some of my best friends to DAV. Can’t really think of much more to write… It’s always great to reminisce those wonderful days at DAV….

This is Rajan and me from 17-02-1999!


This was possibly on 16th Feb, outside ‘Joy’.. what wonderful memories…


Just caught this wonderful poem in a forward; it captures all the nostalgia from the school days:

Gone are the days …

When the school reopened in June,
And we settled in our new desks and benches…

When we queued up in book depot,
And got our new books and notes.

When we wanted two Sundays and no Mondays, yet
managed to line up daily for the morning prayers.

We learnt writing with slates and pencils, and… Progressed To fountain pens and ball pens and then Micro tips…

We began drawing with crayons and evolved to
Colour pencils and finally sketch pens…

We started calculating first with tables and then with
Clarke’s tables and advanced to calculators and computers.

When we chased one another in the corridors in Intervals,
and returned to the classrooms drenched in sweat…

When we had lunch in classrooms, corridors, playgrounds, under the trees and even in cycle sheds.

When all the colors in the world, decorated the campus on the Second Saturdays.

When a single P.T. period in the week’s Time Table was awaited more eagerly than the monsoons.

When cricket was played with writing pads as bats,
And Neckties and socks rolled into balls.

When few played “kabadi” and “Kho-Kho” in scorching sun, While others simply played “book cricket” in the
Confines of classroom.

Gone are the days…
Of fights but no conspiracies,
Of Competitions but seldom jealousy…

When we used to watch Live Cricket telecast,
In the opposite house during Intervals and Lunch breaks.

When few rushed at 3:45 to “Conquer” window seats in
our School bus. While few others had “Big Fun”, “peppermint”, “kulfi”, ” milk ice !” and “sharbat !” at 4 o’Clock…

Gone are the days of Sports Day, and the annual School Day , And the one-month long preparations for them.

Gone are the days Of the stressful Quarterly, Half Yearly and Annual Exams, And the most enjoyed holidays after them.

Of tenth and twelfth standards, when we
Spent almost the whole year writing revision tests…

We learnt, we enjoyed, we played, we won, we lost…
We laughed, we cried, we fought, we thought…

With so much fun in them, so many friends,
So much experience , all this and more…

Sachin ODI Dismissal Stats

These stats are interesting too. Vaas is not too much of a concern, nor Razzaq, as you can see his averages are not that bad against them. But you can conclude that Razzaq dismisses a set Tendulkar, and that’s a bit dangerous. I remember a 93 in Aus, and of course the recent 95 when Razzaq dismissed Sachin. On the other hand, Pollock has always dismissed Sachin early. It can also be viewed that Pollock can’t dismiss Sachin except early! So maybe, Sachin should not open against SA. It’s always possible to draw dumb conclusions from statistics, but we can make useful interpretations at times! Walsh again appears to have had an upper hand with Sachin. I am surprised that Cronje has dismissed Sachin only thrice — at one point it appeared that he was picking Sachin every single game!

Statsguru – SR Tendulkar – ODI Batting – Bowlers/fielders dismissed by

SR Tendulkar (Sachin Tendulkar) [Player Page] – RHB; LBG
Born: 1973-04-24 (present age: 32y 299d)

ODIs: India 1989/90 – 2005/06 (16y 238d – 32y 298d)
Also: Test Player 1989/90 – 2005/06.

Filter: none.
Sort order: total dismissals (descending).

                     Mat    I  NO  Runs HS1  HS2  HS3     Ave 100  50   0
overall              362  353  33 14146 186* 152  146   44.20  39  72  16

Bowler Dis bwd c fi c wk st lbw hit Ave 0 Team WPUJC Vaas (LFM) 9 2 4 2 0 1 0 20.88 1 SL SM Pollock (RFM) 7 2 2 2 0 1 0 6.28 1 SA HH Streak (RFM) 7 1 4 2 0 0 0 32.28 0 Zim Abdul Razzaq (RFM) 6 2 1 2 0 1 0 51.50 0 Pak Azhar Mahmood (RFM) 6 1 3 1 0 1 0 25.83 0 Pak GD McGrath (RFM) 6 0 4 2 0 0 0 26.16 1 Aus CA Walsh (RF) 6 1 3 1 0 1 0 8.66 2 WI Aaqib Javed (RFM) 5 0 3 1 0 1 0 3.20 1 Pak AA Donald (RF) 5 1 3 0 0 1 0 22.60 0 SA DW Fleming (RFM) 5 1 1 3 0 0 0 54.60 0 Aus ST Jayasuriya (SLA) 5 1 2 0 2 0 0 48.20 0 SL DNT Zoysa (LFM) 5 0 3 1 0 1 0 47.40 0 SL AC Cummins (RFM) 4 1 3 0 0 0 0 30.00 0 WI PS de Villiers (RFM) 4 1 3 0 0 0 0 15.50 0 SA CZ Harris (RM) 4 0 3 1 0 0 0 69.75 0 NZ JH Kallis (RFM) 4 1 3 0 0 0 0 74.75 0 SA B Lee (RF) 4 1 3 0 0 0 0 17.25 0 Aus TM Moody (RM) 4 0 4 0 0 0 0 16.25 0 Aus DK Morrison (RFM) 4 1 3 0 0 0 0 12.75 0 NZ M Muralitharan (OB) 4 0 4 0 0 0 0 46.25 0 SL Shoaib Akhtar (RF) 4 0 2 1 0 1 0 36.00 0 Pak Waqar Younis (RF) 4 1 2 1 0 0 0 34.25 1 Pak NW Bracken (LFM) 3 0 1 2 0 0 0 58.00 0 Aus WJ Cronje (RM) 3 0 2 1 0 0 0 28.33 0 SA TJ Friend (RFM) 3 0 1 1 0 1 0 24.66 0 Zim L Klusener (RFM) 3 0 2 1 0 0 0 24.66 0 SA GR Larsen (RM) 3 1 0 0 1 1 0 49.33 0 NZ CR Matthews (RFM) 3 0 0 3 0 0 0 15.66 0 SA Mohammad Sami (RF) 3 0 1 2 0 0 0 14.33 1 Pak DJ Nash (RFM) 3 1 2 0 0 0 0 18.00 0 NZ Shoaib Malik (OB) 3 1 2 0 0 0 0 114.00 0 Pak SA Thomson 3 0 1 2 0 0 0 25.00 1 NZ DR Tuffey (RFM) 3 0 2 1 0 0 0 5.66 0 NZ Wasim Akram (LF) 3 1 2 0 0 0 0 5.00 0 Pak SR Waugh (RM) 3 0 2 0 0 1 0 59.33 0 Aus GP Wickramasinghe (RFM) 3 0 3 0 0 0 0 17.33 0 SL CEL Ambrose (RF) 2 0 0 2 0 0 0 24.00 0 WI Ata-ur-Rehman (RFM) 2 1 1 0 0 0 0 27.50 0 Pak N Boje (SLA) 2 0 1 0 1 0 0 90.50 0 SA EA Brandes (RFM) 2 0 2 0 0 0 0 9.50 0 Zim CL Cairns (RFM) 2 0 1 0 0 1 0 2.50 1 NZ CE Cuffy (RF) 2 0 2 0 0 0 0 33.00 1 WI KSC de Silva (LFM) 2 0 1 1 0 0 0 20.50 0 SL M Dillon (RFM) 2 1 1 0 0 0 0 36.50 0 WI CJ Drum (RFM) 2 0 2 0 0 0 0 1.50 0 NZ CRD Fernando (RFM) 2 0 2 0 0 0 0 19.00 0 SL A Flintoff (RF) 2 1 1 0 0 0 0 43.00 0 Eng GW Flower (SLA) 2 1 1 0 0 0 0 42.00 0 Zim JN Gillespie (RF) 2 0 1 0 0 1 0 31.50 0 Aus MN Hart (SLA) 2 1 1 0 0 0 0 72.00 0 NZ M Hayward (RF) 2 1 1 0 0 0 0 21.50 0 SA PW Jarvis (RFM) 2 2 0 0 0 0 0 14.50 0 Eng MS Kasprowicz (RFM) 2 0 1 0 0 1 0 71.00 0 Aus CC Lewis (RFM) 2 0 2 0 0 0 0 18.50 0 Eng BM McMillan (RMF) 2 1 1 0 0 0 0 39.50 0 SA Mohammad Rafique (SLA) 2 1 1 0 0 0 0 51.00 0 BD Naved-ul-Hasan (RMF) 2 0 1 1 0 0 0 2.50 0 Pak ML Nkala (RFM) 2 1 1 0 0 0 0 28.00 0 Zim RJ Ratnayake (RFM,LB) 2 1 0 0 0 1 0 44.50 0 SL Saqlain Mushtaq (OB) 2 0 0 0 2 0 0 83.50 0 Pak Shahid Afridi (RM,LBG) 2 1 1 0 0 0 0 68.00 0 Pak MA Suji (RMF) 2 0 2 0 0 0 0 11.50 0 Ken A Symonds (RM,OB) 2 0 2 0 0 0 0 74.50 0 Aus ME Waugh 2 0 1 0 1 0 0 76.00 0 Aus