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Results tagged with matrices
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user 89279
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.
0
votes
1
answer
171
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Jordan decomposition of powers of the Shift Matrix [closed]
Given the upper Shift Matrix, which for e.g. dimension $5$ is
$$
{\bf E}_{\,{\bf 5}} = \left( {\matrix{
0 & 1 & 0 & 0 & 0 \cr
0 & 0 & 1 & 0 & 0 \cr
0 & 0 & 0 & 1 & 0 \cr
0 & 0 & 0 & …
- 208
6
votes
Accepted
Inverse of a matrix with binomial entries
Let's refer everything to square matrices indexed from $0$ to $h$, that I will denote as
$$
{\bf M}_{\,h} = \left\| {\;f(n,m)\;} \right\|_{\,h}
$$
with $n$ being the row index and $m$ the column index … \,h} = \;\left\| {\;\left( \matrix{
1 \cr
n - m \cr} \right)\;} \right\|_{\,h} \cr
& \overline {\bf X} = transpose({\bf X}) \cr}
$$
After that the determinant follows easily, since the matrices …
- 208