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), ...

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8
votes
1answer
66 views
+50

Most efficient method for computing Singular Value Decomposition of a triangular matrix?

There are several methods available for computing SVD of a general matrix. I am interested in knowing about the best approach which could be used for computing SVD of an upper triangular matrix. ...
3
votes
0answers
44 views
+50

Eigenvalues of block matrix of order $m+1$

How to find eigenvalues of following matrix? $\begin{bmatrix} mkI-A & -A & -A & \cdots & -A\\ -A & kI-A & O & \cdots & O\\ -A & O & kI-A & \cdots & O\\ ...
1
vote
1answer
27 views
+50

Block matrix of order $m$ with three block matrices

How to find eigenvalues of following block matrices? $M=\begin{bmatrix} A & B & O & O & O & O & O & \cdots & O & O\\ B & A & B & O & O & O ...
2
votes
0answers
35 views
+100

How to prove this result about the interlacing of eigenvalues.

Let $A$ be a real symmetric matrix of order $n$ with eigenvalues $\mu_1\ge \mu_2,\ldots, \mu_{n}$. $B=\begin{bmatrix} x&x&x&x&x \end{bmatrix}$, where $x$ is non zero column vector in ...