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. ... 続きを読む >>

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.... 続きを読む >>

The Rosser matrix is a classic matrix eigenvalue test problem.... 続きを読む >>

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.... 続きを読む >>

An option in eigshow demonstrates SVD, the matrix singular value decomposition. The emphasis is on orthogonality.... 続きを読む >>

Three more examples with eigshow, all of them degenerate in some way or another.... 続きを読む >>

One of my all-time favorite MATLAB examples is eigshow.... 続きを読む >>

This is the third part of a series of posts about Marc Kac's 1966 paper in the American Mathematical Monthly [1]. This part is devoted to the proof that the drums have the same eigenvalues. ... 続きを読む >>

This is the second part of a series of posts about Marc Kac's 1966 paper in the American Mathematical Monthly [1]. This part is devoted to contour plots of the eigenfunctions. ... 続きを読む >>

The title of this multi-part posting is also the title of a 1966 article by Marc Kac in the American Mathematical Monthly [1]. This first part is about isospectrality. ... 続きを読む >>