Cleve’s Corner: Cleve Moler on Mathematics and Computing

Singular Value Analysis of Cryptograms

Posted by Cleve Moler,

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 >>

Reverse Singular Value Decomposition 2

Posted by Cleve Moler,

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 >>

Higher Resolution Penny

Posted by Cleve Moler,

High resolution measurements of the depth of the mold for the United States one cent coin provide an interesting data set.... read more >>

The Tektronix 4081 2

Posted by Cleve Moler,

The Tektronix 4081 minicomputer at Argonne National Laboratory in the summers of 1977 and '78 played an important role in the early development of MATLAB.... read more >>

Surprising SVD, Square Waves, and Pi 2

Posted by Cleve Moler,

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 >>

Magic Stars

Posted by Cleve Moler,

Magic Stars are a little like Magic Squares. My grandson was introduced to them in his junior high school math class.... read more >>

The Rosser Matrix

Posted by Cleve Moler,

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

Fiedler Companion Matrix

Posted by Cleve Moler,

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 Ardent Titan, part 2 2

Posted by Cleve Moler,

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. The second startup was known as Ardent Computer for most of its brief existence.... read more >>

These postings are the author's and don't necessarily represent the opinions of MathWorks.