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. ... 더 읽어보기 >>

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.... 더 읽어보기 >>

The Rosser matrix is a classic matrix eigenvalue test problem.... 더 읽어보기 >>

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.... 더 읽어보기 >>

An option in eigshow demonstrates SVD, the matrix singular value decomposition. The emphasis is on orthogonality.... 더 읽어보기 >>

Three more examples with eigshow, all of them degenerate in some way or another.... 더 읽어보기 >>

One of my all-time favorite MATLAB examples is eigshow.... 더 읽어보기 >>

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. ... 더 읽어보기 >>

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. ... 더 읽어보기 >>

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. ... 더 읽어보기 >>