Lecture 31
Change
of
Basis
of
Compression
Images
Transformations Matrix
Pixel
州
0
xi grayscale
Exit
image
f
256
8bits
512
E
512
n
if
R
2
color
2
hi
3
512
overload
512
JPEG
Joint
Photographic Experts Group
age
X
of basis
⼆
仇焦
n
current
basis
eueg grayscale
o
相近
grayscale 很
Standard
basis
7
記錄 的 pixels
no use
is
ill
Better basis
1
1
vector can completely give
Solid
the
information
on
a
image
Fourier basis
coeffi
8x8
f64
Hill
512
wn
signal p
change the
lossless
2懼
basis
7coeffsc
lossly
compression
512
throw
away
small
weft
threshing
ˇ
不 记⼼
gbe3，4
Video
squenǔduwd
Wavelets
H
lik
Wavelets
i
州
州
Favier
0
lossless
step
P
GW
⼆
find
a
it
⼗
GW8
coefficients
Cg
nwc
吖
111
側
CWP
⼆
lgbasis
g
ui
f些
⼈
p
fast
ǐǜu
inv
LFF
NT
20Few is enough
orthogonal
Orthonormal
WL W
to
good
WO
Wait
find
Ǘ
a
Change
Gwnf
of
basis
W
the
Suppose
it
o
with
it
Dnewbais
basis
have
with
linear
new basis vectors
comb
以
如
Tiuxn
to
respect
has
matrix
respect
has
V1
to
V8
8
W8
wi
matrix
A B What relation
B
conclusion
It
similar
Bin
M
t
change
of
basis
⼼比
家
⼆
w
what is A
I
know
using
in
V8
Tag
CMtwvt.MG V8
GTM
IX
TN
t
GND t.it CHU
anV1 ⼗ Qz Nzt
TNDidahtdzz.LV
a
an
A
u
TND.TN
Tcompktly from
Bacause every X
WVU
basis
taa V8
⼗ in ⼗ GSLV8
an
a i. k
eigenvector basis
Tcu
what
⼆
is
⼈以
A
n.
if
but find in
too expensive
ffee
器
6.3
Mdt
6.4
A
6.5
⼆
Au
et
and
多
AT
Positive definite
6.6
Similar
real
⼀
2enough evectors
BMÀM
3 can find
orthonormal
赢入
点 NÀM
UIÚ
A
6，7
a
Stpl
SVD
器 Au
i
Example
i
u
general solution
比七
⼆
GǙX
tczeixztcj stp2
MX
A
is singular
Hìi
他可find that
A的
⼆
N
八
⼆
0
Ptznw
2入 ⼆ 0
八
Aiantiymmtric
入 pure imaginary
o
Mr
入⼆ 0
坑
上
snj
QU
I
g
ucttcěxitaǚxzt
b
No
at ti
Uco
比
Cz XN
axlt
Geii
t
GX3
aěytaehtaeiy
uu
ftp.e
2Th
Eht
管
ti
Orthogonal
when
AÁ
2以
E it
t
⼆
EN
五元 x
erector
ÁA
Sym
Antisym
Orthogonal
c.ci
I
if
ins
A
uurěù
ětsǒ51
了
y
em
5
IQ
⽇了 以
I
八
⼆
八七
0
八⼆
2
州1 啡 ⼼ 啦
a
diagonaltable
Yes all c.CC
b
doesn't matter
Symmetric
all
a
C
Real
Positive
咖比
no
⼩
semi
Definite
Czo
e
Markov matrix
7
入⼆ 1
其中 ⼀个
others
No
1
因為 要 stable
是 projector
7
九
O.rl CO FP
⼆
orz
firsts
orthogonal vector
value
so
九
三八
value
SVD
3
A
every
orthogonal
Atothngonalkdiag
⼆
UEV ATA_i.lv
uai
Eui
symmuic
VEVT
⼆
⼆
V is the
euectov
Tiìnf
扯
sgni
of
ÁA
Aiiir
NIU
3
2
umpǒyuvzi
⼩
ii
68
a
vector
not
5
in the
I
M
Null Space
NLA
SUD
1
i
V2
NO
4
A
lsymmtric
Orthogonal
九
be
can
sym
IN 1
Orthgmd
1
In
入 is real
i
A posdef
I
Qx
⼼
No
N
IQXHMN IMI
INNH.IN
no
入
⼆
重根
有
对 ⾓化 了
Yes 可
Non singular
Yes
Show 主
Projection
isymmw z.pt
p
肛
is
a
Projection
1
I
ÌHI
i
本
肝 2⽉ 扛
i
i
A⼆⽉ 埔
例 Ortho
f
2⽉
3
A
At Ii
ICHI
A红
ÍCHI
2⼯
I
肛
肛
I
八
入
i
1
2，0
入 1，0_n.eu
