HP 39g+, User Manual

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Matrices 13-13
SVD
Singular Value Decomposition. Factors an
m × n
matrix
into two matrices and a vector:
{[[
m × m
square orthogonal ]],[[
n × n
square orthogonal ]],
[ real ]}.
SVD
( matrix )
SVL
Singular Values. Returns a vector containing the singular
values of
matrix.
SVL
( matrix )
TRACE
Finds the trace of a square matrix. The trace is equal to
the sum of the diagonal elements. (It is also equal to the
sum of the eigenvalues.)
TRACE
( matrix )
TRN
Transposes matrix . For a complex matrix, TRN finds the
conjugate transpose.
TRN
( matrix )
Examples
Identity Matrix
You can create an identity matrix with the IDENMAT
function. For example, IDENMAT(2) creates the 2×2
identity matrix
[[1,0],[0,1]]
.
You can also create an identity matrix using the
MAKEMAT (
make matrix ) function. For example, entering
MAKEMAT(I¼J,4,4) creates a 4 × 4 matrix showing the
numeral 1 for all elements except zeros on the diagonal.
The logical operator ¼ returns 0 when I (the row number)
and J (the column number) are equal, and returns 1 when
they are not equal.
Transposing a
Matrix
The TRN function swaps the row-column and column-row
elements of a matrix. For instance, element 1,2 (row 1,
column 2) is swapped with element 2,1; element 2,3 is
swapped with element 3,2; and so on.
For example,
TRN([[1,2],[3,4]])
creates the matrix
[[1,3],[2,4]]
.