Last week I posted the fiftieth in my “What Is” series of articles. I began the series just over a year ago, in March 2020. The original aim was to provide “brief descriptions of important concepts in numerical analysis and related areas, with a focus on topics that arise in my research”, and the articles were meant to be short, widely accessible, and contain a minimum of mathematical symbols, equations, and citations. I have largely kept to these aims, though for some topics there is a lot to say and I have been more lengthy.

The articles are also available in PDF form on GitHub.

Below is a list of all the “What Is” articles published at the time of writing, in alphabetical order.

If there is a topic you would like me to cover, please put it in the comments below.

- What Is a Block Matrix?
- What Is a Cholesky Factorization?
- What Is a Companion Matrix?
- What Is a Condition Number?
- What Is a Correlation Matrix?
- What is a Diagonally Dominant Matrix?
- What Is a Fractional Matrix Power?
- What Is a Fréchet Derivative?
- What Is a Generalized Inverse?
- What Is a Hadamard Matrix?
- What Is a Householder Matrix?
- What Is a Matrix Function?
- What Is a Matrix Square Root?
- What Is a Matrix?
- What Is a Modified Cholesky Factorization?
- What Is a (Non)normal Matrix?
- What Is a QR Factorization?
- What Is a Random Orthogonal Matrix?
- What is a Sparse Matrix?
- What Is a Symmetric Positive Definite Matrix?
- What Is a Unitarily Invariant Norm?
- What Is an M-Matrix?
- What Is an Orthogonal Matrix?
- What Is Backward Error?
- What Is Bfloat16 Arithmetic?
- What Is Floating-Point Arithmetic?
- What Is IEEE Standard Arithmetic?
- What is Numerical Stability?
- What Is Rounding?
- What Is Stochastic Rounding?
- What Is the Adjugate of a Matrix?
- What is the Cayley–Hamilton Theorem?
- What Is the Complex Step Approximation?
- What Is the CS Decomposition?
- What Is the Gerstenhaber Problem?
- What Is the Growth Factor for Gaussian Elimination?
- What Is the Hilbert Matrix?
- What is the Kronecker Product?
- What Is the Log-Sum-Exp Function?
- What Is the Matrix Exponential?
- What Is the Matrix Logarithm?
- What Is the Matrix Sign Function?
- What Is the Matrix Unwinding Function?
- What Is the Nearest Positive Semidefinite Matrix?
- What Is the Nearest Symmetric Matrix?
- What is the Polar Decomposition?
- What Is the Sherman–Morrison–Woodbury Formula?
- What Is the Singular Value Decomposition?
- What Is the Softmax Function?
- What Is the Sylvester Equation?

These are such a brilliant resource, Nick. Thank you.

What about “what is rank revealing decomposition”? it could be an interesting and useful topic. Tks

Dear Professor Higham,

I would like to read from you about “totally positive matrices” (a subject related to some of your classical contributions; I recall my comment in your post “Conference in Honour of Walter Gautschi”).

Thank you for your work.