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Linear SG review sheet, Summaries of Mathematics

Mathematics

Linear study sheet for review and

Typology: Summaries

2023/2024

Uploaded on 05/05/2025

mary-daniher 🇺🇸

1 document

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Linear

StudyGuide Pro Perp

Criteria

for

Invertibility Odistance x!toline l

Transformations xprojix xE

Iit.fi

niaiisoinotred

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input

vector

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basis

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ftp.r

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space

vs

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space have2linindvectors

pit EEfegtmatrix

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space Feine

dims

3179nutmatter planedimz

pointdime

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andVectors Orthogonal Orthonormal

orthogonal

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iÉi me inverse IE

ai iii

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like b.li

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OR CBIPen

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aim linina

vectors

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repeated Inverse wcot

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multiples

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itge

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rows pirotro comfy.fi

jtlA

it 70Not

invertible

citxo.aeta.es Gs aas nligi

fi

Eti

Aj

EIEitmaies

orthog

basis can

simplify

sina.nl b32 ta

Partial preview of the text

Download Linear SG review sheet and more Summaries Mathematics in PDF only on Docsity!

Linear

Study

Guide

Pro

Perp

Criteria

for

Invertibility

Odistance

x̅

to

line l

Transformations

x projix

x E

I

it.fi

n

iaiis

oinotred

ftp.mitinatcs

niiiiit.in

iinnoo.Rn

n

entriespervector

input

vectorhas

components

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cols

in

aff

pronents

if

Éf

rank

dimicola

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b

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R

has dim2so

basis must

Ég

É

ftp.r

g.arequttofindT

Y Colspace vs Rowspace

have

2 linind

vectors

p

it

EE

fegtmatrix

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dims

317 9

nutmatter

planedimz

point

dime

Eigenvaluesand

Vectors Orthogonal

Orthonormal

orthogonal

compotrowspace

nulla

Rank

A v X

ROWAY

nulla

rattan'IPlts

e cos

i

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me

inverse

IE

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i

ii

État

A

AII

RREEIIA.EEE

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like

b.li

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diagonal

entries critical

pts

inflection

p

eigenvectors

if

j

pen

fbial.ba c

OR

C

B

I

Pen

Rnvs.dim.PE

eaEf nq

n.y

i'bastime

ran

complactor

aim

linina

vectors

alg.mu

t

7imesXisroot repeated

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w

cot

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multiples

geo.mu't

lin indeigen

vectors

itge

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diagonizable

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comfy.fi

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invertible

citxo.aeta.es

Gs

a as

n

ligi

fi

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i

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basis

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sina.nl

b

ta

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Equations

Study

Guide

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squares

x̅

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parameters it deto

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at

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Study

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Linear

Invertibility if

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2 2

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dettoxt

compute

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then A A

I

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ranka

inanity

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inconsient

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u

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n

entries

per

vector

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03 93

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9

v

Rank finind cols pivot

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I

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rank

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vectors

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if

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go

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matrix

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det

o

if

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y Sugix

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iiie

det

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overlap

w

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I

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istait

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I

iii

iiiii

main

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mean

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Fcz

findin factoru

Order

and

linearity

Solve

order

y

F

Smacx

Fthly

ex

y

2nd

order

Fy

N

to

find h

ly

Linear

altly

az

t

y

aolt

y g

t

integrate

to

get hly

C

y

y y

first

power

coeff

of

y

are

functions

in

terms

of

only

y

pixly qlx

y

o redorder

age

is

function

only

in

terms

of

given

y

find

yz

yiy.se

f9ax2Abel'sThm

W

x

Wixpetplxdx

Particular

Solutions

c.sn i

iis

Aesx

Ax

BX

C

es

Ae

sinyx Be

cos4x

lax'tBxC

casux

Dx Ex

F

sinux

Ax

Be

os4x extE

exsinax

Q var of

par

sec

tan

Linear SG review sheet, Summaries of Mathematics

Related documents

Partial preview of the text

Download Linear SG review sheet and more Summaries Mathematics in PDF only on Docsity!

Guide

to

A v X

A

AII

n.y

ran

a as

Differential

Study

Guide

x̅

Atalb

intention

a bi eaxc

A

can

axax

fix

y

be

on't

Guide

Linear

Invertibility if

A

detA

then A A

Rree Ila

Far

Least

tidett

I

x

A

det

O

dim

per

Per

rank

dimcolA

QTA

Q

Gs

inRlinind

and

A

linindnot

pointdimo

P

A

thm

A

if

to

if

ofrowspace

A

mulla

if

diffequ.LY

exiii.in

iiie

det

for

I

Y.fi

istait

9tayitey

I

iii

iiiii

hi

dx

Fcz