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. ... 更多内容 >>

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.... 更多内容 >>

The Rosser matrix is a classic matrix eigenvalue test problem.... 更多内容 >>

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.... 更多内容 >>

An option in eigshow demonstrates SVD, the matrix singular value decomposition. The emphasis is on orthogonality.... 更多内容 >>

Three more examples with eigshow, all of them degenerate in some way or another.... 更多内容 >>

One of my all-time favorite MATLAB examples is eigshow.... 更多内容 >>

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. ... 更多内容 >>

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. ... 更多内容 >>

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. ... 更多内容 >>