EE 16A

Prof. chunter Liu

Feb on. 19

MRI for your bedtime reading

sEhnRISoostehfar"

i.

⇒

'

IncrementalA c- p

n × n

A-'

A = I ;

AAE. Ra -

- 17£-

I}§ ) , RI 's ?

soli. Is¥, g) EiE=-i=i

Sira tart = Isoo . EE.

-

÷:El :::p =

I RE '

±

f-

-IT.

.

' ¥:j

V, Bz

,

t Vz 'Re,TV3 Rts

Ed . A =,

is A invertase.

A' '

?

Theory A is invertible if and only if its colours-

- -

are buoy independent .

show :P if A is invertible ⇒ colons of A are linear

i welp .

③ if A ohms are buy i nd,

⇒ A is inutile

Dealt show

E

i#Ee⇒ omg aha I -0

it than aI

,snow that AT =0

then ,AT -0

,

=' i A-

' A = I.

'

-

by def .

Ohm of A is iud ,

② if A' cows are binary ind ⇒AT =3

⇒ unique Sol.

- n

A ER" "

,It ' b E R

,

>I = BI

, B ← r" '

n

AX = ABI = I ⇒ CAB - I 35=0-

AB - I = o,

BA - IN

To do ;

I ,Vector spares

2.

Matrix rank

Veeru spare-

DI router c.

I ) = gasetofrertusv.eg.ri.ve"

space a set of Sealers F, ay R

,

or C

rules of Liner opera 'm

addition , seen - Vertov multi

rector addition rt + c Jin > = Tutu ) tu.

ass.

Je tu= Je I

J to =P

closure:

I,

I e-

V,

e I C- it

( T , F ) I EF ,2.8=8

diltn-butue.sn ( Ttc > = 2T + aI

closure, I c- T . off ⇒ a FFF

E

,

ituon aer

,Terias

at ?

isI

'

O ? Teri ,inert

8th ?

rear spare I BR ) C t Chuffy.IT)Qiu - it ?

Basis of hector space-

dot Bens of a near spae CJ, I ) is a Set of vets

IT , ,I -

- - In } that sutures

D Ji,

in.

-

. - In are long independents② For V-J EF

,

theres exists sailors

& i , to .- -

, An C- F,

Suit thy

T = AT , take . . - t 2nF

A mum set of hears the can regret all nets in ✓

A basis its not angle .

O I : ( R2 , R ) Hour may bars acts in V ? 2

On is { I , IS a basis ? Sei,

- In } V

Q , .

.SJ , in 3 basis ? Yes

Det Dimension of rear spare is the # of basis

vectors.

* dimension of aviator f R"

,

# of element

a rotor.

Subspace

DE A Sas spare c u , F ) consists of a sunset of the

Set V of the new spae TV ,F ) ,

D contains a zero vector 8 E U

② closed under Vertu addition, ft , ,

It it = THIEU③ closed indefscabs multiplied

, f JEU,

LET,

⇒ 2T EU

If define a J = V in ④ ⇒ inconsistent with D.

I ! if U = span c Ii ),

is ( U,

R ) a sub spare

a,

Ot em ,. , ?

is in.ru?..arsy..su-ot

NO.

H 's not closed.