Matrix functions, such as the exponential, square root and cosine, play an indispensable role in various fields including quantum mechanics, control theory and numerical solution of differential ...

We investigate the matrix function optimization under the orthonormal constraint on the matrix variable. By introducing an index-notation-arrangement-based chain rule (I-Chain rule), we obtain the ...

This article is dedicated to the calculation of matrix functions. Before defining what they are, let's briefly explain what they are not. Suppose we have a sufficiently regular function f and a square ...

A simple matrix class that's compatible with STL functions and CERNs ROOT library. Includes functions for + - * /, inverting, normalisation, eigenvalues, the trace and transpose ...

Many dimensionality reduction methods in the manifold learning field have the so-called small-sample-size (SSS) problem. Starting from solving the SSS problem, we first summarize the existing ...

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SAS/IML software has many built-in functions that generate useful matrices. For example, the J function creates a matrix with a given dimension and element value when you supply the number of rows and ...

These results indicate that matrix biogenesis entails coordinated delivery of the individual matrix polysaccharides. To understand whether coordination occurs at the cellular level or the community ...