This is the third in a series of posts on the finite Fourier transform. The Fourier matrix produces an interesting graphic and has a surprising eigenvalue distribution. ... read more >>

For several years we thought Hadamard matrices showed maximum element growth for Gaussian elimination with complete pivoting. We were wrong. ... read more >>

In rare cases, Gaussian elimination with partial pivoting is unstable. But the situations are so unlikely that we continue to use the algorithm as the foundation for our matrix computations.... read more >>

The Singular Value Decomposition of the digram frequency matrix of a text coded with a simple substitution cypher can reveal information about the vowels and consonants in the text. ... read more >>

Employing a factorization based on the least significant singular values provides a matrix approximation with many surprisingly useful properties. This Reverse Singular Value Decomposition, RSVD, is also referred to as Subordinate Component Analysis, SCA, to distinguish it from Principal Component Analysis. ... read more >>

ContentsTim DavisSparse Matrix VisualizationsMusic VisualizationsMetastaseisBlue MondayElectrodoodleMorning Has BrokenBach Toccata and FugueNotesArt StudioTim DavisAt the recent SIAM conference on... read more >>

I am surprised when many of the singular values of a nonsymmetric variant of the Hilbert matrix turn out to be nearly equal to $\pi$. The explanation involves the Fourier series for a square wave.... read more >>

The Rosser matrix is a classic matrix eigenvalue test problem.... read more >>

The Fiedler companion matrix distributes the coefficients of a polynomial along the diagonals of an elegant pentadiagonal matrix whose eigenvalues are equal to the zeros of the polynomial.... read more >>

The first posting earlier today was truncated. Here is the complete post. Even though I am one of the founders of the MathWorks, I only acted as an advisor to the company for its first five years. During that time, from 1985 to 1989, I was trying my luck with two Silicon Valley computer startup companies. Both enterprises failed as businesses, but the experience taught me a great deal about the computer industry, and influenced how I viewed the eventual development of MATLAB. This post continues the discussion of the Intel Personal Supercomputer... read more >>