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Status: Tags: #cards/math232/unit6 Links: Matrix

Diagonalization

Principles

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Similar Matrices ?

• When $P^{-1}AP = B$ for some invertible matrix $P$ ** Trace of A ?
• tr(A) = $a_{11}$ + $a_{22}$ + … + $a_{nn}$

If A,B (- R such that $P^{-1}AP = B$ for some invertible matrix $P$, then $A$ and $B$ have the same ?

• Determinant
• Eigenvalues
• Rank
• Trace

Theorems

A matrix is diagonalizable iff every eigenvalue of the matrix has ?

• geo mult = alg mult

If A (- R has n distinct eigenvalues, then ;; A is diagonalizable

Diagonalization Theorem

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• Square matrix A is only diagonalizable iff a basis for $R^n$ exists that consists of eigenvectors of $A$

Examples

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References:

Created:: 2022-03-14 04:31