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Lecture 23

# MATH 235 Lecture 23: Inner Product, Length, and Orthogonality

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University of Massachusetts Amherst

Mathematics

MATH 235

Yaping Yang

Spring

Description

4/25/2017
Sect
5.1 Inner Product, Length
Orthogonal
nher Product in
Rn dot product
nX1
un V
theorem
for
CER
E Rn
(cemmulative)
(distributive)
u W
20, any
Inner Product Length
Len
(norm)
magnitude)
def.: a Vector
V is caled a unt us 1.
find a und vector u in the same direction as V
ex let
Spa
Subsbace.
find a unit vectsr that is a basis of W
4/25/2017 Sect 5.1 Inner Product, Length Orthogonal nher Product in Rn dot product nX1 un V theorem for CER E Rn (cemmulative) (distributive) u W 20, any Inner Product Length Len (norm) magnitude) def.: a Vector V is caled a unt us 1. find a und vector u in the same direction as V ex let Spa Subsbace. find a unit vectsr that is a basis of WSO
could also usc
d V
did
an
CCA
us- vs)
ER
sa
u, V
U and
V ate orth
(porpondicular
Theorem
U and V an orthogonal
ER
et Z
et W subspace
is W (2 W) if
def
Z l Sr every
VE W
ortho
der
Com blemen
na
RN
fact: W is
over
(0, 0, 0)
R3, let W
span i mal vector
the p
fact dim w t din W
Comes firm dim
(Al)
rank (A) n
RT, let W
WI
plane t

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