FoDA19"

Singular Lake-

composition⇐ SUD)

Inputmatrix A ⇐ Rmd / Goal B k-dimensional

subspaced columns VB= { vi. Ve, n.vn }A • Hui /1=1 VIEIRA

• Hi,

U;] =o jti;i- c-Rd

au osoai

93

Tor

ss-t-a.B-I://ai-q.ca"

E- I K

Ttslai )= ¥, u;

c- IRMA

*¥÷÷÷÷¥÷÷÷.

" .

- → sins .

Will - lt :%÷÷÷¥÷÷÷÷÷:÷÷:j=inxd him singular0 values

uj

vector.

114-11=1Lv; ,Wi_- 0 its raid

" shape"

of A via SVD

✗

::÷¥¥÷¥÷:÷÷:RdA- ✗ 11

☐- i

•Wait vector

✗ = (0.243, 0.970)

v,v2 A-✗ = USVT#C p -VA

ftp.fcv.ir, 4K¥

P•→ 11PM -1

q=SVT×÷÷E¥É¥÷÷⇒f- Sp ⇐R"

Best-R-k-prgxVB-G.ua . . He }

Terror for one dapfa point ae|Rd%

" - " "d

completed te z bag

:S

t.la - IT,s( a)112--1/44-4,0;D - Evita

.vn//1Rdi--ii-a-TEhZ--aZ-bZ=H&dvi2a.ui>IT a

*¥÷É,

j-1-+1 pythagorean= É < a ,vjYj=t-11

11^-41=-1/9:÷¥]H=É⇐:*> 'E- I

HA - ITBCAIH! É Hai - Fist.it/--SSE( A.B)F- I

n d d

= & Cai ,y.>2) = & HAV;1i=Ée-= ,(¥É+\ j-k.li f- KH

top Krsuect =

arsmin SSECA,B)

of A 13=-14. . .ve}

sk-d.mn#in--A--rant of B - K

"min 11A - A-Me

Ak =best rant# approximation of Ate

Ate = & Tj Ujvjt = Quill ? + Tzu ,zVzT+ . . .

F- 1 sifaka RSV c-IR"d

, rankl

* = """¥÷"Fun I

Sn - diag (r, . . -%)An - ST its just not

j=1 KA -Aid,¥ - É rior j-K-11

= U stilt11A - Antti -- +7 , 11kt -A.)✗IT

= Ur Srvpt= Tk?H