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)

2
votes
0answers
39 views
+50

How is the pseudo-inverse of $A \oplus A$ related to psueod-inverse of A

Let $A$ be a real $2n \times 2n$ diagonalizable real matrix. I can write $A$ as the product $A= UV$ where $U$ and $V$ are real symmetric matrices where $U$ is block diagonal with $I_{n \times n}$ as ...
6
votes
4answers
199 views
+50

Find a matrix with determinant equals to $\det{(A)}\det{(D)}-\det{(B)}\det{(C)}$

Assume I have 4 matrices $A,B,C,D\in\Bbb{R}^{n\times n}$. I want to build a matrix $E\in\Bbb{R}^{m\times m}$ such that: $$\det{(E)}=\det{(A)}\det{(D)}-\det{(B)}\det{(C)}$$ under the following ...