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Sometimes when doing regression analysis, we estimate our function $g(x) = E(Y |X =x )$ using an orthonormal series, and in particular we use an approximate series $g_{p_n}(x) = \sum_{k=1}^{p_n} ... 1answer 193 views Lower bounds on matrix eigenvalues Let$A$be a real$n\times n$matrix and let$\mu_1, \dots, \mu_n$the (generalized, complex) eigenvalues of$A$. Assume that$$0 < \alpha < \mathrm{Re}(\mu_1) < \dots < ... 0answers 48 views Possible diagonal values of a product of matrices with some specific characteristics Hello all, This is a question that might or might not be related to my previous one. Imagine you have two matrices: Matrix$\mathbf{\Phi}=[\Phi_1,\ldots,\Phi_M]\in\mathbb{R}^{L\times M}$where ... 1answer 192 views A spectral radius inequality Define$\rho(A)$to be the spectral radius of a square matrix$A$. Let$S$and$T$be two non-negative square matrices and$h$a real number such that$\rho(S+T) < h$. Show that$\rho((hI-S)^{-1}T) ...
Hello, Let $A_n = (a_{k-j};\;k,j = 0,1,\ldots,n-1)$ be a sequence of $n\times n$ Toeplitz matrices, with eigenvalues $(\lambda_{n,i};\;i = 0,1,\ldots,n-1)$. If $A_n$ were a sequence of Hermitian ...