HP HP-15C Advanced Functions Handbook

Section 4: Using Matrix Operations
99
distance between matrices A and B is the norm of their difference,
denoted || A — B||. The norm can also be used to define the condition
number of a matrix, which indicates how the relative error of a
calculation compares to the relative error of the matrix itself.
The HP-15C provides three norms. The Frobenius norm of a matrix
A, denoted || A\\, is the square root of the sum of the squares of the
matrix elements. This is the matrix analog of the Euclidean length
of a vector.
Another norm provided by the HP-15C is the row norm. The row
norm of an m X n matrix A is the largest row sum of absolute
values and is denoted | A||^:
A D= max
Ki<n
ft.
/ Jq,:,-|.
The column norm of the matrix is denoted ||A||^ and can be
computed by || A||c = || AT||^. The column norm is the largest column
sum of absolute values.
For example, consider the matrices
A —
Then
and
1 2 3
459
A-B
and B
222
456
|| A - B\\ = VlT« 3.3 (Frobenius norm),
|| A — Bll^ = 3 (row norm), and
|| A — B||c = 4 (column norm).
The remainder of this discussion assumes that the row norm is
used. Similar results are obtained if any of the other norms is used
instead.
The condition number of a square matrix A is defined as
Then 1 ^ K(A) < °° using any norm. The condition number is

HP HP-15C Specifications

General

Brand	HP
Model	HP-15C
Category	Calculator
Language	English