List questions from diagonalization

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Finding $C$ such that $C^TAC=$diag$(I_k,-I_l,O)$ (Diagonal form)

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Prove that if A is an upper triangular matrix with distinct values on the main diagonal, then A is diagonalizable.

Published on 10 Jul 2019 - 20:15

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I'm not getting a diagonal matrix when I use spectral decomposition on this matrix

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$A$ and $A^2$ have same characteristic polynomial

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Maximum of det(AX) as a function of Tr(AX)

Published on 14 Jul 2019 - 7:04

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Let $f:L \rightarrow L$ be a diagonalizable operator.

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Graph Fourier transform: the adjoint notation for the eigenbasis matrix

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Show that if A is diagonalizable and 1 and −1 are the only eigenvalues of $A$, then $A^{-1 }= A$.

Published on 18 Jul 2019 - 5:34

229

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Find the principal axes $y_{1}$ and $y_{2}$ diagonalizing the quadratic form $q = x_{1}^{2} + 8x_{1}x_{2} + x^{2}_{2} $

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273

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$A^5 = A$ is diagonalizable, $A - \overline A^{T}$ is diagonalizable

Published on 20 Jul 2019 - 5:27

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Analogy of Jordon Normal Form for Antilinear Maps

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Upper Triangular and Diagonal Matrices

Symmetric matrix (completing the square/diagonal form)

Kronecker-Weierstrass problem, 3x6 matrices conjugacy or congruent classes?

Finding $C$ such that $C^TAC=$diag$(I_k,-I_l,O)$ (Diagonal form)

Eigenvalues of sum of two matrices

Prove that if A is an upper triangular matrix with distinct values on the main diagonal, then A is diagonalizable.

I'm not getting a diagonal matrix when I use spectral decomposition on this matrix

$A$ and $A^2$ have same characteristic polynomial

Maximum of det(AX) as a function of Tr(AX)

Let $f:L \rightarrow L$ be a diagonalizable operator.

Graph Fourier transform: the adjoint notation for the eigenbasis matrix

Show that if A is diagonalizable and 1 and −1 are the only eigenvalues of $A$, then $A^{-1 }= A$.

Find the principal axes $y_{1}$ and $y_{2}$ diagonalizing the quadratic form $q = x_{1}^{2} + 8x_{1}x_{2} + x^{2}_{2} $

$A^5 = A$ is diagonalizable, $A - \overline A^{T}$ is diagonalizable

Analogy of Jordon Normal Form for Antilinear Maps

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