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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
 •...
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This document was uploaded on 03/04/2014 for the course CH 354L at University of Texas at Austin.

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