Status: Tags: #cards/math232/unit8/1 Links: Diagonalization
Diagonalization of symmetric matrices
Principles
Symmetric matrix ?
- x(Ay) = (Ax)y for all x,y
Theorems
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- Can use to find Diagonalization matrix easily
All symmetric matrices are orthogonally diagonalizable, which can be proved using the Principal Axis Theorem
Examples
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- Observe orthogonality
Find an orthogonal matrix that diagonalizes $A=
\begin{pmatrix}
1 & -2 \\-2 & 1
\end{pmatrix}$
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Orthogonally diagonalize the matrix $A = \begin{pmatrix}
5 & -4 & -2 \\-4 & 5 & -2 \\-2 & -2 & 8
\end{pmatrix}
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References:
Created:: 2022-03-31 16:31