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SemidefiniteProgramming :: smat2vec

smat2vec -- vectorization of a symmetric matrix

Synopsis

Usage:

v = smat2vec A

A = vec2smat v
Inputs:
- A, a matrix, symmetric
- v, a matrix, a vector
Optional inputs:
- Scaling => ..., default value 1
Outputs:
- v, a matrix
- A, a matrix

Description

The method smat2vec obtains the vectorization of a symmetric matrix. The method vec2smat performs the reverse operation.

i1 : A = matrix(QQ, {{1,2,3,4},{2,5,6,7},{3,6,8,9},{4,7,9,10}})

o1 = | 1 2 3 4  |
     | 2 5 6 7  |
     | 3 6 8 9  |
     | 4 7 9 10 |

              4        4
o1 : Matrix QQ  <--- QQ

i2 : v = smat2vec A

o2 = | 1  |
     | 2  |
     | 3  |
     | 4  |
     | 5  |
     | 6  |
     | 7  |
     | 8  |
     | 9  |
     | 10 |

              10        1
o2 : Matrix QQ   <--- QQ

i3 : vec2smat v

o3 = | 1 2 3 4  |
     | 2 5 6 7  |
     | 3 6 8 9  |
     | 4 7 9 10 |

              4        4
o3 : Matrix QQ  <--- QQ

The scaling of the off-diagonal entries can be controlled with the optional parameter.

i4 : smat2vec(A,Scaling=>2)

o4 = | 1  |
     | 4  |
     | 6  |
     | 8  |
     | 5  |
     | 12 |
     | 14 |
     | 8  |
     | 18 |
     | 10 |

              10        1
o4 : Matrix QQ   <--- QQ

Ways to use `smat2vec` :

"smat2vec(List)"
"smat2vec(Matrix)"

For the programmer

The object smat2vec is a method function with options.