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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]].