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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.

5 votes
1 answer
416 views

positive hermitian elements in $M_n(\mathbb{C})$

Elements of the set $P$ of positive hermitian $n×n$ matrices over complex numbers have some special properties: (i) they are closed under sum, (ii) they are closed under multiplication by positive scalars …
spelas's user avatar
  • 179
2 votes
0 answers
135 views

Possible restrictions on generators of $M_n(\mathbb{C})$

Suppose matrices $a$ and $b$ generate $M_n(\mathbb{C})$. I would like to know what restrictions this imposes on $a$ and $b$. …
spelas's user avatar
  • 179
1 vote
0 answers
221 views

Centralizer in a matrix algebra over commutative polynomials

Let $A=M_n(F[x_{ij}\mid 1\leq i,j\leq n])$ be the matrix algebra over commutative polynomials in $n^2$ variables $x_{11},\dots,x_{nn}$ over a (nice enough) field $F$. I would like to know what is the …
spelas's user avatar
  • 179