Section 18 Matrix Operation: Mathematical

18.1 Matrix operation

Function	Explanation	Example..x.is.square.matrix.
t	Transpose	t(x)
diag	Diagonal	diag(x)
%*%	Inner (dot) product of two vectors t(x) and y, and conventional matrix multiplication	x %*% y
%o%	Outer product of two vectors x and t(y)	x %o% y
crossprod	Cross products t(x) and y	crossprod(x,y)
tcrossprod	Cross products x and t(y)	tcrossprod(x,y)
det	Determinant	det(x)
solve	Inverse	solve(x)
eigen	Eigenvalues and eigenvectors	eigen(x)
svd	Singular value decomposition	svd(x)
qr	QR decomposition	qr(x)
chol	Choleski decomposition	chol(x)

18.2 Example 1

x <- matrix(c(7, 2, 5, 9), nrow=2, ncol=2)
x+5
x-5
x*5
x/2
x^2
-x
x > 3

18.3 Example 2

# Elementwise operation
x <- matrix(c(7, 2, 5, 9), nrow=2, ncol=2)
y <- matrix(c(3, 9, 5, 7), nrow=2, ncol=2)
t(x)
diag(x)
solve(x)
det(x)
t(x) %*% y