Hessenberg reduction

Performs Householder transformations since a Hessenberg matrix is obtained. A Hessenberg matrix is a matrix of the form

open parentheses table row cell a subscript 11 end cell cell a subscript 12 end cell cell a subscript 13 end cell midline horizontal ellipsis cell a subscript 1 left parenthesis n minus 1 right parenthesis end subscript end cell cell a subscript 1 n end subscript end cell row cell a subscript 21 end cell cell a subscript 22 end cell cell a subscript 23 end cell midline horizontal ellipsis cell a subscript 2 left parenthesis n minus 1 right parenthesis end subscript end cell cell a subscript 2 n end subscript end cell row 0 cell a subscript 32 end cell cell a subscript 33 end cell midline horizontal ellipsis cell a subscript 3 left parenthesis n minus 1 right parenthesis end subscript end cell cell a subscript 3 n end subscript end cell row 0 0 cell a subscript 43 end cell midline horizontal ellipsis cell a subscript 4 left parenthesis n minus 1 right parenthesis end subscript end cell cell a subscript 4 n end subscript end cell row 0 0 0 down right diagonal ellipsis cell a subscript 5 left parenthesis n minus 1 right parenthesis end subscript end cell cell a subscript 5 n end subscript end cell row vertical ellipsis vertical ellipsis vertical ellipsis vertical ellipsis vertical ellipsis vertical ellipsis row 0 0 0 cell a subscript left parenthesis n minus 1 right parenthesis left parenthesis n minus 2 right parenthesis end subscript end cell cell a subscript left parenthesis n minus 1 right parenthesis left parenthesis n minus 1 right parenthesis end subscript end cell cell a subscript left parenthesis n minus 1 right parenthesis n end subscript end cell row 0 0 0 0 cell a subscript n left parenthesis n minus 1 right parenthesis end subscript end cell cell a subscript n n end subscript end cell end table close parentheses

hessenberg_reduction(Matrix))

Given a matrix, transforms it to a Hessenberg matrix.

Below is a complete list of options that may be used in the hessenberg_reduction function.


Option Description Format Default value
exact_computations We can choose to perform or not exact computations. {exact_computations=false} true, but depends on the input