submatrix notation

Let n and k be integers with 1kn. Denote by Qk,n the totality of all sequences of k integers, where the elements of the sequence are strictly increasingPlanetmathPlanetmath and choosen from {1,,n}.

Let A=(aij) be an m×n matrix with elements from some set, usually taken to be a field for ring. Let k and r be positive integers with 1km, 1rn, αQk,m and βQr,n. We let α=(i1,,ik) and β=(j1,,jr)

The submatrixMathworldPlanetmath A[α,β] has (s,t) entry equal to aisjt and has k rows and r columns.

We denote by A(α,β) the submatrix of A whose rows and columns are complementary to α and β, respectively.

We can also define similarly the notations A[α,β) and A(α,β].

Title submatrix notation
Canonical name SubmatrixNotation
Date of creation 2013-03-22 16:13:36
Last modified on 2013-03-22 16:13:36
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 5
Author Mathprof (13753)
Entry type Definition
Classification msc 15-00