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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
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
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
Principal Values of Inverse Cosine and Related Functions
I’ve recently been working, with Mary Aprahamian, on theory and algorithms for the matrix inverse sine and cosine and their hyperbolic counterparts. Of course, in order to treat the matrix functions we first need a good understanding of the scalar … Continue reading
Making Sense of Multivalued Matrix Functions with the Matrix Unwinding Function
Try the following quiz. Let be an real or complex matrix. Consider the principal logarithm—the one for which has imaginary part in —and define for (an important special case being for an integer ) . True or false: for all … Continue reading