Matrices, determinants and the birth of Linear Algebra | Math History | NJ Wildberger

The solution to a system of equations goes back to ancient Chinese mathematics--a treatise called the Nine Chapters of the Mathematical Arts. In this video we discuss the further history of this problem and the natural connection with the theory of determinants.

Major contributors include Leibniz, Cramer, Laplace, Vandermonde, Cauchy, Cayley and Sylvester. In particular we look at Cramer's Rule, Laplace's expansion of determinants, resultants as described by Euler and Bezout, and then Sylvester's reformulation of these polynomials as determinants.

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[paulmanmoy]

I am from India...Sir thank u for ur knowledge... I don't know why ur channel is not growing rapidly... I shares all of ur videos...

[BrianBechtel]

Great Series. I think the history of Mathematics is a very interesting topic and I appreciate how you approach the subject.

[ManikRaina]

1:00 - Nine Chapters of the Mathematical Arts, Seki Kowa, Leibniz
3:00 - Matrices from system of linear equations
5:00 - Determinants: unique solution
7:14 - Cramer's rule: Solution of a system of linear equations
9:25 - Cramer's motivation: Conic through 5 points
14:21 - Computing a determinant
16:08 - Parity theorem (Cauchy)
19:35 - Vandermonde's method
21:36 - Laplace expansion
24:50 - Multiplicativity of determinants (A.L Cauchy)
26:10 - J.J Sylvester - common solutions of polynomial equations
37:19 - Sylvester's resultant formula
41:00 - Determinants as volume, Cayley Hamilton theorem, Eigen values and vectors

[lumri]

It was amazing that the ancient Chinese mathematicians use only counting rods as aiding device when solving matrix problems.

[tinkeringtim]

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[helioshyperion]

Great lecture!
I would like to suggest that you should do a series on geometric algebra. It would be a perfect fit for this channel, and the coverage on the topic is sorely lacking on youtube.
Keep up the good work!

[rickshafer]

This is good. I mean this blows away any linear algebra course. He is giving you First Principles .

[tauceti]

Thank you for this. I just naturally love history. And Math is quite fun too. Combining them is just beautiful!

[Tommy_]

Regarding the resultant: If the determinant of the coefficient matrix is 0, there can't be a unique solution to the system. In other words, it is NOT enough to know that the system has AT LEAST one suloution. So how do you conclude that the determinant (giving the resultant) is 0?

[JohnDoe-khhy]

I removed the number of the beast fron your likes. No need to thank me, sir