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HP 48g Graphing Calculator User Manual

Page 173

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Commands for Characterizing Matrices (continued)

Key

Programmable

Command

Description

S R R D

SRAD

Command. Returns the spectral radius

of a square matrix. The spectral radius
is the absolute value of the largest
eigenvalue of the matrix.

C 0 hi D

COND

Command. Returns the column-norm

condition number of a square matrix.

The condition number is defined to be

the product of the column norm of a
square matrix and the column norm of
its inverse.

R fl H K

RANK

Command. Returns an estimate of the

rank of a matrix. The rank of a matrix

is equal to the number of nonzero

singular values of the matrix. If Flag

—54 is clear (default), RANK treats any

computed singular value less than 10"^^
times the size of the largest computed
singular value as zero. If Flag —54 is

set, RANK counts all nonzero singular
values no matter their size.

DET

DET

Command. Returns the determinant of

a square matrix. DET checks flag —54,

and will refine its computed value only

if —54 is clear (default).

1 k r-i i . 1-

TRACE

Command. Returns the trace of a

square matrix. The trace of a matrix is
equal to the sum of the diagonal
elements and also equal to the sum of
the eigenvalues of the matrix.

14

Matrices and Linear Algebra 14-9

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