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These functions are described next. Because many of these functions use
concepts of matrix theory, such as singular values, rank, etc., we will include
short descriptions of these concepts intermingled with the description of
functions.
Function ABS
Function ABS calculates what is known as the Frobenius norm of a matrix. For
a matrix
A
= [a
ij
]
m
×
n
, the Frobenius norm of the matrix is defined as
∑∑
=
=
=
n
i
m
j
ij
F
a
A
1
1
2
If the matrix under consideration in a row vector or a column vector, then the
Frobenius norm , ||
A
||
F
, is simply the vector’s magnitude. Function ABS is
accessible directly in the keyboard as
„Ê
.
Try the following exercises in ALG mode (using the matrices stored earlier for
matrix operations):
Function SNRM
Function SNRM calculates the Spectral NoRM of a matrix, which is defined as
the matrix’s largest singular value, also known as the Euclidean norm of the
matrix. For example,
