- TODO: change of basis for vectors and for transformations.
- TODO: Dot product: algebraic and geometric definitions, their equivalence.
- TODO: trace
- TODO: Projection vs idempotent
- Nilpotent matrices
- Cramer’s rule
- Superlearn
TODO: change of basis for vectors and for transformations.
TODO: Dot product: algebraic and geometric definitions, their equivalence.
TODO: trace
https://en.wikipedia.org/wiki/Trace_(linear_algebra)
The trace of a nilpotent matrix is zero: https://math.stackexchange.com/questions/1220470/trace-of-a-nilpotent-matrix-is-zero
TODO: Projection vs idempotent
Let $P$ a projection operator, $P^2 = P$. Show $V = \operatorname{Im}P \oplus \operatorname{Ker}P$
https://math.stackexchange.com/questions/261704/show-that-the-direct-sum-of-a-kernel-of-a-projection-and-its-image-create-the-or
Nilpotent matrices
https://en.wikipedia.org/wiki/Nilpotent_matrix
$J(0)$ is the simplest example.
Cramer’s rule
https://en.wikipedia.org/wiki/Cramer's_rule
Inverse of matrix using Cramer’s rule:
http://pi.math.cornell.edu/~andreim/Lec17.pdf
Geometric interpretation: https://www.youtube.com/watch?v=jBsC34PxzoM