Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with matrices
Search options not deleted
user 91764
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.
14
votes
Determinant of a $k \times k$ block matrix
Subtracting the last row of blocks from the first $k-1$ rows of blocks, we obtain
$$\begin{bmatrix}A-B & O & O & \dots & O & B-A\\ O & A-B & O & \dots & O & B-A\\ O & O & A-B & \dots & O & B-A\\ \vdo …
10
votes
Accepted
Decomposing a matrix into a product of sparse matrices
In other words, we left-multiply $\mathrm A$ by permutation matrices (whose inverses are their transposes) and by elementary matrices of the form
$$\mathrm E_{ij} := \mathrm I_n + \beta_{ij} \, \mathrm … Hence, the larger $n$, the sparser the matrices. …
9
votes
Is there a name for matrices of the form $a_{ij}=\frac{1}{a_{ji}}$?
Note that you are considering currency exchange matrices where $R_{ij} R_{ji} = 1$, which one could call perfect currency exchange matrices. … I would have written $R_{ij} R_{ji} \leq 1$ instead, in order to include the (reciprocal) perfect currency exchange matrices, too. …
7
votes
Accepted
Finding Toeplitz matrix nearest to a given matrix
M_2, \dots, \mathrm M_n$ are $n \times n$ symmetric Toeplitz basis matrices. … Let $\mathrm M_1 = \mathrm I_n$ correspond to the main diagonal, whereas the remaining basis matrices correspond to super and sub diagonals. …
7
votes
Accepted
What is the term for this type of matrix?
When $b = 0$, we have an $n \times n$ symmetric arrowhead matrix. When $b \neq 0$, we have
$$\begin{bmatrix}
c & c & c & \cdots & c & c \\
c & a & b & \cdots & b & b \\
c & b & a & \cdots & b & b \\
…
6
votes
Accepted
Minimization problem involving the inverse of an affine matrix function
Rephrasing slightly, given (symmetric) matrix $\mathrm A \succeq \mathrm O_n$, we have the following minimization problem in (symmetric) matrix $\mathrm X \succeq \mathrm O_n$
$$\begin{array}{ll} \te …
5
votes
Do these matrices have a name?
the Sylvester construction
$$\mathrm H_{2k} = \begin{bmatrix} \mathrm H_k & \mathrm H_k\\ \mathrm H_k & -\mathrm H_k\end{bmatrix} \qquad \qquad \qquad \mathrm H_1 = 1$$
which builds (symmetric) Walsh matrices …
5
votes
Is this inequality involving the Frobenius norm right?
Given $\mathrm A \in \mathbb R^{m \times n}$ and $\mathrm B \in \mathbb R^{n \times p}$, let $\mathrm B \mathrm B^{\top} = \mathrm Q \Lambda \mathrm Q^{\top}$ be an eigendecomposition of $\mathrm B \m …
5
votes
Accepted
Positive definite matrices diagonalised by orthogonal matrices that are also involutions
Let $n \times n$ matrix $\rm A$ be symmetric and positive definite. Since $\rm A$ is symmetric, it is diagonalizable. Hence, there exists a (non-singular) matrix $\rm P$ such that $\mathrm A = \mathrm …
5
votes
Large power of an adjacency matrix
Since the adjacency matrix $\mathrm A$ is not symmetric, we have a directed graph.
Given a positive integer $k$, the $(i,j)$-th entry of $\mathrm A^k$ gives us the number of directed walks of lengt …
4
votes
Solving $\text{trace}\left[\left(I + pY\right)^{-1} \left(I - p^{2}Y\right)\right] = 0$ for ...
The product of two upper triangular matrices is also upper triangular with the main diagonal being the entrywise product of the main diagonals of the factors. …
4
votes
Nontrivial lower bound on the sum of matrix norms
Let function $f : \mathbb R^{m \times n} \to \mathbb R_0^+$ be defined as follows
$$f (\mathrm X) := \| \,\mathrm X \mathrm A^\top \|_\text{F}^2 + \| \,\mathrm X^\top \mathrm A \,\|_\text{F}^2 + \lef …
3
votes
Determinant of a $k \times k$ block matrix
Let us assume that $A-B$ is invertible. Write
$$\begin{array}{rl} C &= \begin{bmatrix} A & B & \ldots & B\\ B & A & \ldots & B\\ \vdots & \vdots & \ddots & \vdots\\B & B & \ldots & A\end{bmatrix}\\\\ …
3
votes
Symmetric linear least-squares solution
Complementing Denis Serre's answer and rephrasing the original problem slightly, given tall matrices $\rm A$ and $\rm B$, we have the following quadratic program in square matrix $\rm X$
$$\begin{array …
2
votes
Integral of the entrywise square of the exponential of a matrix
Given a Hurwitz matrix $\mathrm A \in \mathbb R^{n \times n}$, let
$$\Phi (t) := \exp(\mathrm A t)$$
be the state transition matrix, and let its $(i,j)$-th entry be denoted by
$$\varphi_{ij} (t) := …