So what's the point of linear algebra, anyway? (opens in new tab)

(chittur.dev)

4 points3PS1y ago5 comments

5 comments

People have written very nice books on this e.g.

https://linear.axler.net/

3PSOP1y ago

> The novel approach taken here banishes determinants to the end of the book.

Big fan of this approach! Though I have warmed up to determinants ever since I saw 3Blue1Brown give a fairly intuitive explanation for them [0].

I'm kind of curious as to how they covered eigenvalues/the characteristic polynomial without determinants. Maybe they just jumped straight to diagonalization?

[0] https://www.youtube.com/watch?v=Ip3X9LOh2dk

richrichie1y ago

One does not need determinant to define eigenvalues. For example:

If T is a linear operator on vector space V, a scalar a is an eigenvalue if there is a v in V s.t. Tv = av.

This is the approach the book takes.

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5 comments

richrichie1y ago

People have written very nice books on this e.g.

https://linear.axler.net/

3PSOP1y ago

> The novel approach taken here banishes determinants to the end of the book.

Big fan of this approach! Though I have warmed up to determinants ever since I saw 3Blue1Brown give a fairly intuitive explanation for them [0].

I'm kind of curious as to how they covered eigenvalues/the characteristic polynomial without determinants. Maybe they just jumped straight to diagonalization?

[0] https://www.youtube.com/watch?v=Ip3X9LOh2dk

richrichie1y ago

One does not need determinant to define eigenvalues. For example:

If T is a linear operator on vector space V, a scalar a is an eigenvalue if there is a v in V s.t. Tv = av.

This is the approach the book takes.

1 more reply

j / k navigate · click thread line to collapse