Fifty “What Is” Articles

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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.

  1. What Is a Block Matrix?
  2. What Is a Cholesky Factorization?
  3. What Is a Companion Matrix?
  4. What Is a Condition Number?
  5. What Is a Correlation Matrix?
  6. What is a Diagonally Dominant Matrix?
  7. What Is a Fractional Matrix Power?
  8. What Is a Fréchet Derivative?
  9. What Is a Generalized Inverse?
  10. What Is a Hadamard Matrix?
  11. What Is a Householder Matrix?
  12. What Is a Matrix Function?
  13. What Is a Matrix Square Root?
  14. What Is a Matrix?
  15. What Is a Modified Cholesky Factorization?
  16. What Is a (Non)normal Matrix?
  17. What Is a QR Factorization?
  18. What Is a Random Orthogonal Matrix?
  19. What is a Sparse Matrix?
  20. What Is a Symmetric Positive Definite Matrix?
  21. What Is a Unitarily Invariant Norm?
  22. What Is an M-Matrix?
  23. What Is an Orthogonal Matrix?
  24. What Is Backward Error?
  25. What Is Bfloat16 Arithmetic?
  26. What Is Floating-Point Arithmetic?
  27. What Is IEEE Standard Arithmetic?
  28. What is Numerical Stability?
  29. What Is Rounding?
  30. What Is Stochastic Rounding?
  31. What Is the Adjugate of a Matrix?
  32. What is the Cayley–Hamilton Theorem?
  33. What Is the Complex Step Approximation?
  34. What Is the CS Decomposition?
  35. What Is the Gerstenhaber Problem?
  36. What Is the Growth Factor for Gaussian Elimination?
  37. What Is the Hilbert Matrix?
  38. What is the Kronecker Product?
  39. What Is the Log-Sum-Exp Function?
  40. What Is the Matrix Exponential?
  41. What Is the Matrix Logarithm?
  42. What Is the Matrix Sign Function?
  43. What Is the Matrix Unwinding Function?
  44. What Is the Nearest Positive Semidefinite Matrix?
  45. What Is the Nearest Symmetric Matrix?
  46. What is the Polar Decomposition?
  47. What Is the Sherman–Morrison–Woodbury Formula?
  48. What Is the Singular Value Decomposition?
  49. What Is the Softmax Function?
  50. What Is the Sylvester Equation?

3 thoughts on “Fifty “What Is” Articles

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

  2. 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.

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