This preview shows page 1. Sign up to view the full content.
Unformatted text preview:
at A = ( ⎛1 2⎞
A= ⎜
⎝3 4⎟
⎠ ⎛1 2⎞
35⎜
=
⎝3 4⎟
⎠ ) ( 3 ⋅1 + 5 ⋅ 3 3 ⋅ 2 + 5 ⋅ 4 ) = ( 18 26 ) ⎛ 1 2 ⎞ ⎛ 3 ⎞ ⎛ 1 ⋅ 3 + 2 ⋅ 5 ⎞ ⎛ 13 ⎞
Aa = ⎜
=
=
3 4 ⎟ ⎜ 5 ⎟ ⎜ 3 ⋅ 3 + 4 ⋅ 5 ⎟ ⎜ 29 ⎟
⎝
⎠⎝
⎠⎝
⎠⎝
⎠ • Note
that
atA
is
diﬀerent
from
Aa.
They
are
the
same
only
if
the
matrix
A
is
symmetric,
i.e.
A*ij=Aji
Vector
matrix
Mul2plica2on:
More
examples
• atAa=?
( ⎛ 1 2 ⎞⎛ 3 ⎞
35⎜
⎟⎜ 5 ⎟ =
⎝ 3 4 ⎠⎝
⎠ ) ( ⎛ 3⎞
18 26 ⎜
⎟ = 54 + 130 = 184
⎝5⎠ ) Symmetric
Matrices
• Symmetric
matrices
(Aij=Aji)
is
something
we
will
be
very
interested
in.
Example
⎛3 2⎞
A( symmetric) = ⎜
2 4⎟
⎝
⎠ • A
special
symmetric
matrix
is
the
iden2ty
⎛1 0⎞
I =⎜
⎝0 1⎟
⎠ • For
all
A
of
the
same
dimension
as
I
we
have
IA = AI = A Eigenvectors
and
Eigenvalues
•...
View
Full
Document
This document was uploaded on 03/04/2014 for the course CH 354L at University of Texas at Austin.
 Spring '06
 henkelman

Click to edit the document details