# Tagged Questions

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### Computations for LDA: Eigendecomposition

While reading the book Elements of Statistical Learning p. 113, the author used eigendecomposition of the covariance matrix $\hat{\Sigma}_k =\mathbf{U}_k\mathbf{D}_k\mathbf{U}_k^T$ where ...
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### How to find eigenvalues of the following block circulant matrix

I have a block matrix of size PN x PN of the form: Where A and C are P x P matrices. I would like to find the eigenvalues of the matrix B, that is where
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### Same eigenvalue spectrum with different matrices

There are two matrices $D$ and $T$ which provides eigenvalue spectrum (dispersion relation) according to $$E(K) = \operatorname{eig}(D + T \exp(iK) + T' \exp(-iK))$$ $$K = 0:dK:\pi$$ Where K is a ...
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### Diagonalization of sparse block matrix

I have a real symmetric matrix, $$\left( \begin{array}{ccc} 0 & M & M' \\ M ^T & 0 & 0 \\ M ^{ \prime T} & 0 & 0 \end{array} \right)$$ ...
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### Estimate eigenvectors of symmetric matrix with almost vanishing diagonal

Is there a way to approximate the eigenvectors of a symmetric matrix with almost vanishing diagonal elements, i.e. with the block matrix form, M=\left( \begin{array}{cc} ...
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### Eigenvalues of a block matrix

For $X=\left(\begin{array}{cc} A & B\\ C & 0 \end{array}\right)$ , how are eigenvalues of X related to eigenvalues of A ?
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### Eigenvalue of anti triangular block matrix (skew matrix?)

I have an real anti-triangular matrix $M=\left[ \begin{array}{cc} A & B \\ I & 0 \\ \end{array} \right]$ where I is an identity matrix. $A$, $B$, $I$, $0$ are all square real ...
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### Why a (general) block matrix does not have the same eigenvalues of the first block?

Based on the next relation: $$\det\begin{bmatrix}A & B \\ C & D\end{bmatrix} = \det(A)\det(D - CA^{-1}B),$$ I have that for computing the eigenvalues of the block matrix: ...
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### Checking if one “special” kind of block matrix is Hurwitz

I have the next block matrix $$J = \begin{bmatrix}A & B \\ K &0\end{bmatrix}$$ all matrices are square, where $A < 0$ (definite negative), $B$ has all its eigenvalues with positive real ...
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### Eigenvalue decomposition of block covariance matrix for Canonical Correlation Analysis (CCA)

Edited: My question is related to a tutorial I was reading. The covariance matrix is a block matrix where $C_{xx}$ and $C_{yy}$ are within-set covariance matrices and $C_{xy} = C_{yx}^T$ are ...
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### Is eigenvectors/eigenvalues of symetric matrix related with eigenvectors/eigenvalues of its block?

$A$ is square symmetric matrix as: $$A=\begin{pmatrix} A_1&A_2 \\ A_3 & A_4 \end{pmatrix}$$ I have two points which need help to understand clearly: All blocks $A_1$, $A_2$, $A_3$, $A_4$ ...
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### Eigen values of sum of two matrices

I have a following block matrix \begin{align*} M_1 &= M_a + M_b\\\ M_a &= \begin{pmatrix} a_{11} & 0 &b_{13}\\\ 0 & a_{22}& b_{23}\\\ b_{13}^T & b_{23}^T & d_{33} ...
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### Eigen value of a complex block matrix

I have a following block matrix M1 =([a11 a12;a21 a22] [b13;b23];[b13;b23]' d33) + ([c -cr]'*[c -cr] 0;0 I) now what i observe is that whether i use ...
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Thanks guys for the previous answer, Now suppose if I have a matrix e.g $$M_1 = \begin{pmatrix} \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} & B \\ B' & D ... 2answers 200 views ### Eigen value of a block matrix I have following block matrices:$$M_1 = \left(\begin{array}{cc}A & B\\B' & D\end{array}\right)$$and$$M_2 = \left(\begin{array}{cc}A & -B\\-B' & D\end{array}\right) I want to ...
Suppose I have a special block, Hermitian matrix $H = \begin{bmatrix} A & B \\ B^* & A^* \end{bmatrix}$, where * denotes conjugate transpose. The blocks $A$ and $B$ are themself Hermitian in ...
Having a real square $n \times n$ symmetric matrix $B$ (which consists of 2 square blocks of positive numbers and 2 rectangular blocks of negative numbers) I want a real diagonal matrix $D$ such that ...