cIRT (version 1.3.3)

direct_sum: Direct Sum of Matrices

Description

Computes the direct sum of all matrices passed in via the list.

Usage

direct_sum(x)

Value

Matrix containing the direct sum of all matrices in the list.

Arguments

x

A field<matrix> or list containing matrices

Author

James Joseph Balamuta

Details

Consider matrix \(A\) (\(M \times N\)) and \(B\) (\(K \times P\)). A direct sum is a diagonal matrix \(A (+) B\) with dimensions \((m + k) x (n + p)\).

Examples

x = list(matrix(0, nrow = 5, ncol = 3),
         matrix(1, nrow = 5, ncol = 3))
direct_sum(x)

x = list(matrix(rnorm(15), nrow = 5, ncol = 3),
         matrix(rnorm(30), nrow = 5, ncol = 6),
         matrix(rnorm(18), nrow = 2, ncol = 9))
direct_sum(x)