HP MLIB User's Guide Vol. 2 7th Ed.

654 HP MLIB LAPACK User’s Guide
What you need to know to use these subprograms
The norm-computing auxiliary subprograms in LAPACK will evaluate the
1-, ∞-, Frobenius-, or ∆-norms of a matrix stored in a variety of forms, shown in
Table 11-1.
Table 9-1 Norms of Vectors and Matrices
The Frobenius matrix norm is not subordinate to the Frobenius vector norm.
The ∆ matrix norm is not subordinate to any vector norm, nor is it consistent
with itself as a matrix norm.
Name Vector Norm Matrix Norm
1-norm
2-norm
∞-norm
Frobenius norm
∆-norm —
x
1
x
i
i
∑
= A
1
max
j
a
ij
i
∑
=
x
2
x
i
2
i
∑
()
12⁄
=
A
2
max
x 0≠
Ax x⁄=
x
∞
max
i
x
i
=
A
∞
max
i
a
ij
j
∑
=
x
F
x
2
=
A
F
a
ij
2
ij
∑
()
12⁄
=
A
∆
max
ij
a
ij
=