(b). Use the results in (a), show that n min|₁ - Psxi||²/2 = SESM i=1 min VMEVM ZERXM min ||X-ZV where VM = {VM = [v₁, ..., UM] € Rd×M : vŢvt = 1s=t}.
(b). Use the results in (a), show that n min|₁ - Psxi||²/2 = SESM i=1 min VMEVM ZERXM min ||X-ZV where VM = {VM = [v₁, ..., UM] € Rd×M : vŢvt = 1s=t}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Just (B) pls
![(a). We assume that {ø1,.., ¢m} C Rd are a set of orthonormal vectors (i.e., ̟ ¢̟ = 1,=t) and let S be
the subspace spanned by {¢1,…., ¢m}. Please show that for any x E Rd,
M
||r – Psæ|} = min
-
21,...ZMER
k=1
and show that
n
n
M
2
Ellæ; –
Psæ;| =
min
(zik)ie(n],k€[M]
i=1
i=1
k=1
(b). Use the results in (a), show that
n
min x; – Psæ;|} = „min
min ||X – ZV?,
-
SESM
i=1
VMEVM ZER" ×M
where Vm = {V M = [v1,.., VM] E R¢×M : vJv¿ = 1s=t}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe25d54d0-9a14-4be1-a977-6ed5dee4cd4f%2F58cd3b9f-4099-4876-af0d-2705cc3727f1%2Faqf9v6h_processed.png&w=3840&q=75)
Transcribed Image Text:(a). We assume that {ø1,.., ¢m} C Rd are a set of orthonormal vectors (i.e., ̟ ¢̟ = 1,=t) and let S be
the subspace spanned by {¢1,…., ¢m}. Please show that for any x E Rd,
M
||r – Psæ|} = min
-
21,...ZMER
k=1
and show that
n
n
M
2
Ellæ; –
Psæ;| =
min
(zik)ie(n],k€[M]
i=1
i=1
k=1
(b). Use the results in (a), show that
n
min x; – Psæ;|} = „min
min ||X – ZV?,
-
SESM
i=1
VMEVM ZER" ×M
where Vm = {V M = [v1,.., VM] E R¢×M : vJv¿ = 1s=t}.
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