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Results tagged with matrices
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user 496243
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
3
votes
2
answers
388
views
Monotonicity of matrix conjugation
Let $A$ and $B$ be positive-definite matrices such that $A \le B.$
By matrix monotonicity of the root, this also implies that $A^{\alpha} \le B^{\alpha}$ for $\alpha \in [0,1].$
I am now curious under …
5
votes
2
answers
715
views
Matrices with same eigenvalues
It would for instance follow if we can write the matrices as $C_1 = AB$ and $C_2= BA$, but I don't see how such a decomposition could work. … In particular, this does not seem to be restricted to 5x5 matrices but holds for arbitrary matrices of the above form. …
3
votes
1
answer
293
views
Eigenvalues two-fold degenerate
Consider the matrix $$A:=\left(
\begin{array}{cccc}
0 & a & 0 & 0 \\
f & 0 & b & 0 \\
0 & e & 0 & c \\
0 & 0 & d & 0 \\
\end{array}
\right)$$
I noticed that if I square this matrix then the eigenv …
1
vote
1
answer
126
views
Matrix transformation that always works?
.$$
That there exists one such matrix for each set of coefficients is clear, since the eigenvalues of the two $3x3$ matrices are the same. I am looking for one that works for all choices. …