For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), ...

learn more… | top users | synonyms (2)

5
votes
0answers
69 views
+50

Simplifying Trace of a Matrix Expression ${\rm Tr} \left( (I- D^{-1} BA^2) B (I- D^{-1} BA^2)^T \right)$

Let $B$ be a symmetric invertible matrix and let $A$ be a diagonal matrix with non-zero entries on the main diagonal. I am trying to simplify the following expression \begin{align} {\rm Tr} \left( ...
0
votes
1answer
53 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 = \...