Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [matrix-calculus]

Matrix calculus is about doing calculus, especially derivative and infinite series over spaces of vectors and matrices.

Matrix calculus studies derivatives and differentials of scalar, vector and matrix with respect to vector and matrix. It has been widely applied into different areas such as machine learning, numerical analysis, economics etc.

There are basically two methods.

  • Direct: Regard vectors and matrices as scalar so as to compute in the usual way in calculus. And The Matrix Cookbook provides a lot of basic facts.

  • Component-wise: Write everything in indices notation and compute in the usual way componentwisely. Einstein summation convention is frequently used.

3828 questions
-1
votes
1 answer

Proof that the product of a symmetric matrix and its transpose is also symmetric

If A is a symmetric matrix, then verify that A×A' (transpose) and also A'×A is also symmetric
Pp Broski
  • 1
-1
votes
1 answer

Is my statement correct?

I was reading up on the inverse function theorem and I was wondering if the following thought I had was correct: If $f: \mathbb{R}^n \to \mathbb{R}^n$ $g: \mathbb{R}^n \to \mathbb{R}^n$ are eachothers inverse functions and $f,g$ are both…
github
  • 3
-1
votes
1 answer

What is $\nabla_A \epsilon^TA^T(AA^T)^{-1}A\epsilon$?

Let $q$ be the multivariate Normal distribution $\mathcal{N}(\mu, \Sigma)$ and $x$ be a sample from $q$. Hence, $x$ can be written as $$x = \mu + A\epsilon \,, \Sigma = AA^T\,, \epsilon \sim \mathcal{N}(0, I)$$ and $I$ represents the identity…
user2808118
  • 678
-2
votes
1 answer

calculation of the exponent of a matrix

Could you, please, help me to understand what I am doing wrong: I am calculating exp(A), where A=[-1 0;0 -1] By my calculation with series, I got [1/e -1,0;0, 1/e-1]. Matlab and Wolfram give me [1/e,1;1;1/e]. Rules in Perko "differential…
user314849
  • 95
-3
votes
2 answers

partial derivatives of matrix

I have trouble in calculating partial derivatives of matrix recently. The problem is described as following \begin{align} \frac{\partial \log \det\left({\mathbf{I}+\mathbf{\Sigma Q}}\right)}{\partial \mathbf{Q}} \end{align} where $\mathbf{I}$ is…
Qiuyun.Zou
  • 371
1 2 3
…
13
14