Miscellaneous | 128!: |
128!:0 y |
QR. Produces the QR decomposition of a complex matrix y
(in the domain of matrix inverse %.),
an Hermitian matrix and a square upper triangular matrix,
individually boxed.
x=: +/ . * Matrix product A=: j./?. 2 7 4$10 A random complex matrix $A 7 4 'Q R'=: 128!:0 A $Q 7 4 $R 4 4 >./|,(=i.4) - (+|:Q) x Q Q is Hermitian 6.33846e_16 0~:R R is upper triangular 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 A -: Q x R 1 |
128!:1 y | R Inv. Invert square upper triangular matrix. |
x 128!:2 y | Apply. x 128!:2 y applies the verb in string x to y .
For example:
'+/' 128!:2 i.2 5 5 7 9 11 13 '+/' 128!:2"1 i.2 5 10 35 '+/"1' 128!:2 i.2 5 10 35 ('+/';'|.';'|."1') 128!:2&.><i.2 5 +-----------+---------+---------+ |5 7 9 11 13|5 6 7 8 9|4 3 2 1 0| | |0 1 2 3 4|9 8 7 6 5| +-----------+---------+---------+ '2 3' 128!:2 i.2 5 |syntax error | '2 3' 128!:2 i.2 5 '@' 128!:2 i.2 5 |syntax error | '@' 128!:2 i.2 5The ranks of 128!:2 are 1 _ , that is, apply the lists in the left argument to the right argument in toto. |