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Both linear algebra and calculus are classic introductory math classes. A lot of calculus IS linear algebra, given that derivations are linear approximations.

selimthegrim 4y ago
Derivatives are (derivations are the generalization so of course are but I would be surprised to see an undergrad class treat them)
- auggierose 4y ago
  My mistake. I meant derivatives.
sshlocalhost98 4y ago
Yea, theorems like least square prove that A^T * A * X = A^T * B. but how exactly is this related to calculus though?
- peterhalburt33 4y ago
  The equations you quoted result from minimizing the square of the norm of the residual of Ax-b over all inputs x, so in a sense least squares is just calculus…
  - sshlocalhost98 4y ago
    Thanks @peterhalburt33
- selimthegrim 4y ago
  Transposes correspond to integration by parts, and the question of whether A^T*A has an inverse can get involved. Also for infinite matrices the analogies hold more readily, see the observation due to Alan Edelman on page 8 of https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf
  - sshlocalhost98 4y ago
    Thanks @selimthegrim.
chalst 4y ago
I had three years of high school with a substantial amount of calculus; by contrast while I was introduced to matrices and Gaussian elimination at high school, the treatment of the algebraic side was almost completely superficial and focussed on solving systems of linear equations. At university that changed, with a clear treatment of vector spaces and linear algebra as generally interesting topics. But still, they received far less time than calculus in my first year in a maths degree. Now that was over 30 years ago and things might be a bit different today. But I have the impression that the more generally applicable subject of linear algebra gets less time unless students get interested in the applications that demand it be taught properly.

selimthegrim 4y ago

Derivatives are (derivations are the generalization so of course are but I would be surprised to see an undergrad class treat them)

auggierose 4y ago
My mistake. I meant derivatives.

sshlocalhost98 4y ago

Yea, theorems like least square prove that A^T * A * X = A^T * B. but how exactly is this related to calculus though?

peterhalburt33 4y ago
The equations you quoted result from minimizing the square of the norm of the residual of Ax-b over all inputs x, so in a sense least squares is just calculus…
- sshlocalhost98 4y ago
  Thanks @peterhalburt33
selimthegrim 4y ago
Transposes correspond to integration by parts, and the question of whether A^T*A has an inverse can get involved. Also for infinite matrices the analogies hold more readily, see the observation due to Alan Edelman on page 8 of https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf https://klein.mit.edu/~gs/papers/Paper5_ver7.pdf
- sshlocalhost98 4y ago
  Thanks @selimthegrim.

chalst 4y ago

I had three years of high school with a substantial amount of calculus; by contrast while I was introduced to matrices and Gaussian elimination at high school, the treatment of the algebraic side was almost completely superficial and focussed on solving systems of linear equations. At university that changed, with a clear treatment of vector spaces and linear algebra as generally interesting topics. But still, they received far less time than calculus in my first year in a maths degree. Now that was over 30 years ago and things might be a bit different today. But I have the impression that the more generally applicable subject of linear algebra gets less time unless students get interested in the applications that demand it be taught properly.