Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

learn more… | top users | synonyms (1)

0
votes
1answer
60 views
+50

Rank and null space of a particular block matrix.

Let $D_1, D_2 \in \mathbb{R}^{N \times N}$ be diagonal matrices with diagonals that are linearly independent vectors. Let $A, B \in \mathbb{R}^{N \times N}$ be rank-deficient matries. Define $S = \...
5
votes
0answers
44 views
+50

Is it Possible to Show that the Determinant of a Symplectic Matrix is 1 Using Induction?

We have for a $2 \times 2$ matrix $A$ that $A$ is symplectic if and only if $\det A =1$. Is there any way to use this fact as the base for an inductive proof of the fact that the determinant of any ...
2
votes
0answers
45 views
+50

Moore-Penrose pseudoinverse and Linear relations

I recently came across this website called Graphical Linear Algebra. I feel like there's a lot of insight there, but it's too monolithic for me to be able to extract it by skimming. Episode 27 is ...