denotes the set of subsp

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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Let A be a symmetric n x n matrix with eigenvalues
A₁ ≤ 1₂ ≤ ≤n. If Vk denotes the set of subspaces of R" of dimension k, then
λ =
x Ax
min
WEVn-k+1 *EW,x70x¹x
max
x¹ Ax
Xk
= min max
WEVIEW,270 xx
Transcribed Image Text:Let A be a symmetric n x n matrix with eigenvalues A₁ ≤ 1₂ ≤ ≤n. If Vk denotes the set of subspaces of R" of dimension k, then λ = x Ax min WEVn-k+1 *EW,x70x¹x max x¹ Ax Xk = min max WEVIEW,270 xx
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