(3 An nxn matrix P is orthogona) if and only if its celumn vectors form an orthonormal set, (So on ortheg Enal matrix is invertible.] Theor am Let A be an nxn matrix, Then there exists an orthogonal matrix P and a diagonal matrix D such'thet A=p"DP if and Only it A is symmetric, 司 Find on orthoganal matrix P Let A = and a diagenal matrix D such thet A=P'DP. Hiat: Just find the eigen values and Zornesponding eigenvectors for A to eanstruct P

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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() An nxn matrix P is orthogona) if and only
if its column vectors 'form an orthonormal
set. [So on ortheg Bral matrix is invertible.f
Thesr am Let A be an nxn mãtrix, Then there
exists an orthogonal matrix P and a
matrix D such'thet A=p"DP if and Only
jf A is symmetric,
diagenal
Let A =
Find on orthogenel matrix P
and a diagenal matrix D such thet A=p'DP.
Hhat: Just find the eigen values and
Zornesponkeng eigenvectors for A to canstruct P.
Transcribed Image Text:() An nxn matrix P is orthogona) if and only if its column vectors 'form an orthonormal set. [So on ortheg Bral matrix is invertible.f Thesr am Let A be an nxn mãtrix, Then there exists an orthogonal matrix P and a matrix D such'thet A=p"DP if and Only jf A is symmetric, diagenal Let A = Find on orthogenel matrix P and a diagenal matrix D such thet A=p'DP. Hhat: Just find the eigen values and Zornesponkeng eigenvectors for A to canstruct P.
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