Matrix Math

This article gives a brief review of matrix algebra, introduces the concept of the exponential of a matrix, and derives a useful identity for the derivative of the inverse or determinant of a matrix with respect to one of its components.

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Revision history

2023-02-12 (removed an incorrect statement from the new footnote)
2023-02-10 (added a footnote about an alternative definition of eigenvalue)
2022-06-11 (updated references to other articles in this series to link to html abstract pages instead of to pdfs. Didn't change the version number/date)
2022-02-20 (in the null-rotation example: clarified one sentence and added an equation)
2022-02-18 (added a null-rotation example, reformatted to avoid a page break)
2022-02-06 (fixed inconsistent notation in derivation of derivative of inverse matrix)
2022-02-05 (first version)

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updated 2025-06-29

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Matrix Math

Revision history