# numericalImage -- Image of a matrix

## Synopsis

• Usage:
V = numericalImage(M, tol)
• Inputs:
• M, ,
• tol, , a positive number, the numerical tolerance
• Optional inputs:
• Tolerance => ..., default value null, the tolerance of a numerical computation
• Outputs:
• V, ,

## Description

Computes the image of a matrix M numerically using singular value decomposition.

 i1 : M = matrix {{1., 0, 1}, {0, 1, 1}, {1, 0, 1}} o1 = | 1 0 1 | | 0 1 1 | | 1 0 1 | 3 3 o1 : Matrix RR <--- RR 53 53 i2 : numericalImage(M, 0.01) o2 = | -.627963 -.325058 | | -.459701 .888074 | | -.627963 -.325058 | 3 2 o2 : Matrix RR <--- RR 53 53

Singular values less than the tolerance are treated as zero.

 i3 : M = matrix {{0.999, 2}, {1, 2}} o3 = | .999 2 | | 1 2 | 2 2 o3 : Matrix RR <--- RR 53 53 i4 : numericalImage(M, 0.01) o4 = | -.707036 | | -.707177 | 2 1 o4 : Matrix RR <--- RR 53 53

## Ways to use numericalImage :

• "numericalImage(Matrix)"
• "numericalImage(Matrix,Number)"

## For the programmer

The object numericalImage is .