Linear Algebra - Lecture 25 - The Invertible Matrix Theorem

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In this lecture, we discuss The Invertible Matrix Theorem, which is a list of 12 equivalent statements that classify when a square matrix is invertible.
  1. James Hamblin
  2. linear algebra
  3. matrix
  4. invertible
  5. theorem
  6. equivalent
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Комментарии
Автор

Thank you for making videos. There are so little resources online for learning Linear Algebra its astounding. Could you please make sure to put emphasis on proofs? My textbook (Larson's Elementary Linear Algebra) seems prove every proof by saying "We'll leave it to you"

RandmAnclrew
Автор

Statement f and I says the same thing is onto and one-to-one? is this true?

huipingyang
Автор

Also in 9.31 statements I and F together are implying that the transformation t is both onto and one to one.Are you implying that one to one is in a sense, onto?since by definition, onto is when one output is given by AT LEAST one input?

chenlecong
Автор

7.21 it seems like you are implying that e sub i is one of the column of the identity matrix.then x must’ve been the column of the inverse of A.then you’re already assuming A has an inverse matrix and is thus invertible?sorry mate, really don’t get it.

chenlecong
Автор

I don't understand proving g to a😓😓 can anyone please explain??

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