Prml Mathematical Notation
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PRML Mathematical notation M-1
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April 25, 2008
1/6
O8aK
yQ, (calculus)$~Aet (linear algebra)$N( }@ (probability theory) KD$F"kxYN}rO ,W • \qNE4OtX*J7)5rIa9k3HGO J/pC50rA(k3HG"k • \qGOlS7?=-!rHCF$k?a$&f @8N=-H[Jklg,"k •
2/6
qN*J=-
sY/Hk'm<^zN.8z\V'T • Ts'm<^zNg8z\
•
1
M
1
M
T
3/6
qN*J=-
'DhV • (a, b] = {x|a < x ≤ b}'8+&DhV • M × M N1LTs'I %.,ND$FO i = j Nlg$I = 1%l} i 6= j Nlg$I = 0 • FXt (functional)'f [y]$=Nf y(x) OXt • g(x) = O(f (x))'x → ∞ Nlg$|f (x)/g(x)| O -&%?H(P g(x) = 3x + 2 H9lP$ •
[a, b] = {x|a ≤ x ≤ b}
M
ij
ij
2
g(x) = O(x2 )
4/6
qN*J=-
QtO x Nlg$Xt f (x, y) N|TM' E [f (x, y)]%b7QtKD$F@NG"klg$ J,9k • Qt z K*1k x NroU-N(,[Nlg$X t f (x) N|TM'E [f (x)|z] • QtO x Nlg$Xt f (x) N,6'var[f (x)] • QtOY/HkNlg$&,6Ts cov[x, y]%C K cov[x, x] O cov[x] Hq/ •
x
x
5/6
qN*J=DNM x , . . . , x $=Nf x = (x , . . . , x ) r 1DTs X H=-9k%Ts X N n TN.,O TY/Hk x KP~9k • x O 1 !5NQtNlg$N DNM x , . . . , x r 1DNTs x Hq/%x'N !5$x'D !5 •
N
N
1
D
1
T
th
T n
1
N
6/6
!W$S
April 25, 2008
1/6
O8aK
yQ, (calculus)$~Aet (linear algebra)$N( }@ (probability theory) KD$F"kxYN}rO ,W • \qNE4OtX*J7)5rIa9k3HGO J/pC50rA(k3HG"k • \qGOlS7?=-!rHCF$k?a$&f @8N=-H[Jklg,"k •
2/6
qN*J=-
sY/Hk'm<^zN.8z\
•
1
M
1
M
T
3/6
qN*J=-
'DhV • (a, b] = {x|a < x ≤ b}'8+&DhV • M × M N1LTs'I %.,ND$FO i = j Nlg$I = 1%l} i 6= j Nlg$I = 0 • FXt (functional)'f [y]$=Nf y(x) OXt • g(x) = O(f (x))'x → ∞ Nlg$|f (x)/g(x)| O -&%?H(P g(x) = 3x + 2 H9lP$ •
[a, b] = {x|a ≤ x ≤ b}
M
ij
ij
2
g(x) = O(x2 )
4/6
qN*J=-
QtO x Nlg$Xt f (x, y) N|TM' E [f (x, y)]%b7QtKD$F@NG"klg$ J,9k • Qt z K*1k x NroU-N(,[Nlg$X t f (x) N|TM'E [f (x)|z] • QtO x Nlg$Xt f (x) N,6'var[f (x)] • QtOY/HkNlg$&,6Ts cov[x, y]%C K cov[x, x] O cov[x] Hq/ •
x
x
5/6
qN*J=DNM x , . . . , x $=Nf x = (x , . . . , x ) r 1DTs X H=-9k%Ts X N n TN.,O TY/Hk x KP~9k • x O 1 !5NQtNlg$N DNM x , . . . , x r 1DNTs x Hq/%x'N !5$x'D !5 •
N
N
1
D
1
T
th
T n
1
N
6/6
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