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)

5
votes
3answers
95 views
+50

Reflection relating two subspaces

Let $S_1, S_2 \subseteq \mathbb{R}^n$ be two linear $k$-dimensional subspaces. Does there always exist a hyperplane $H$ such that $S_1 = R_H S_2$, where $R_H$ denotes the orthogonal reflection across $...
2
votes
1answer
105 views
+50

Connection of two objects in coordinate system

Please take a look at the following picture: I want to connect two objects by a line. This line has to start and end on an the red lines of the objects and are not allowed (at least it should be ...
2
votes
0answers
34 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 ...
5
votes
3answers
155 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 ...