# Some examples of matrix computations
#
# Create a 3*2 matrix
> A <- matrix(c(1,3,2,5,6,4),byrow=T,ncol=2)
> A
     [,1] [,2]
[1,]    1    3
[2,]    2    5
[3,]    6    4
# Create a 2*2 matrix
> B <- matrix(c(2,2,3,1),byrow=T,ncol=2)
> B
     [,1] [,2]
[1,]    2    2
[2,]    3    1
# Matrix multiplication
> A%*%B
     [,1] [,2]
[1,]   11    5
[2,]   19    9
[3,]   24   16
# Square each element of a matrix
> B^2
     [,1] [,2]
[1,]    4    4
[2,]    9    1
# Multiply a square matrix by itself
> B%*%B
     [,1] [,2]
[1,]   10    6
[2,]    9    7
# Extract the diagonal of a square matrix
> diag(B)
[1] 2 1
> sum(diag(B))
[1] 3
# Concatenate a matrix (i.e. stack the columns)
> c(A)
[1] 1 2 6 3 5 4
# Transpose a matrix
> t(A)
     [,1] [,2] [,3]
[1,]    1    2    6
[2,]    3    5    4 
# Bind the columns of two matrices
> cbind(t(A),B)
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    2    6    2    2
[2,]    3    5    4    3    1