# Tag Archives: matrix_function

## What Is a Matrix Function?

If you give an array as the argument to a mathematical function in a programming language or problem solving environment you are likely to receive the result of applying the function to each component of the array. For example, here … Continue reading

## What Is the Matrix Exponential?

The exponential of a square matrix is defined by the power series (introduced by Laguerre in 1867) That the series converges follows from the convergence of the series for scalars. Various other formulas are available, such as The matrix exponential … Continue reading

Posted in what-is | Tagged | 1 Comment

## What Is a Matrix Square Root?

A square root of an matrix is any matrix such that . For a scalar (), there are two square roots (which are equal if ), and they are real if and only if is real and nonnegative. For , … Continue reading

Posted in what-is | Tagged | 3 Comments

## Improved MATLAB Function Sqrtm

The MATLAB function sqrtm, for computing a square root of a matrix, first appeared in the 1980s. It was improved in MATLAB 5.3 (1999) and again in MATLAB 2015b. In this post I will explain how the recent changes have … Continue reading

## The Improved MATLAB Functions Expm and Logm

The matrix exponential is a ubiquitous matrix function, important both for theory and for practical computation. The matrix logarithm, an inverse to the exponential, is also increasingly used (see my earlier post, 400 Years of Logarithms). MATLAB R2015b introduced new … Continue reading