numericalImage -- Image of a matrix

Usage:

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

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 a method function with options.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/NumericalLinearAlgebra.m2:346:0.