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HP HP-15C Advanced Functions Handbook

HP HP-15C
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1 02
Section
4:
Using Matrix Operations
and A + AA is
singular.
The
figures below illustrate these ideas.
In
each
figure
matrix
A
and
matrix
S are
shown
relative
to the
"surface"
of
singular
matrices
and
within
the
space
of all
matrices. Distance
is
measured
using
the
norm. Around every matrix
A is a
region
of
matrices
that
are
practically indistinguishable
from
A
(for
example, those within
rounding
errors
of A). The
radius
of
this region
is
||AA||.
The
distance
from
a
nonsingular matrix
A to the
nearest singular
matrix
S
is
I/HA"1!.
In the
left
diagram,
||AA||
JC(A)||AA||/||A||«l),then
<
i/llA'1!!.
if
||AA||
«
I/\\A-I\\r
relative variation
in A
1
=
||change
in A
=
(radius
of
sphere)/(distance
to
surface)
In the
right
diagram, ||AA||
>
I/HA"1!).
In
this
case,
there
exists
a
singular matrix
that
is
indistinguishable
from
A, and it may not
even
be
reasonable
to try to
compute
the
inverse
of A.

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HP HP-15C Specifications

General IconGeneral
BrandHP
ModelHP-15C
CategoryCalculator
LanguageEnglish

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