Matrices

variable <- matrix(value, rows, columns); 

This statement assigns to variable a matrix initialized with value of size row by columns.

M[i,j] accesses to the (i,j) element of a matrix M.
M[i,] accesses to the ith row of M.
M[,j] accesses to the jth column of M.

Indexing starts at [1,1].

Binary operations +, - ,* , / work on matrices on an element by element basis. If two matrices are not the same size, then the smaller matrix values are "recycled".

%*% is used for matrix multiplication and matrix vector multiplication. Solution of matrix equations (e.g. matrix "division") is accomplished using the solve(M, B) command.

In addition to constructing matrix elements by looping over the indices, one can use cbind(...) and rbind(...) to create a row by "binding" together rows or columns.

Useful matrix commands

t(M)	Returns the transpose of M.
dim(matrixVariable)	Returns the row and column dimensions of matrixVariable as a vector of integers
diag(...)	The diag command can be used to extracts matrix diagonals, as well as create diagonal matrices.. See diag for details.
%*%	Matrix - matrix and matrix-vector multiplication. Dimensions are checked prior to evaluation.
solve(M, B)	Returns solution of M-1 B. See the original documentation solve for command variants.
qr	Computes the qr factorization of a matrix. See qr for details.
eigen	Computes the eigenvalues and eigenvectors of a matrix. See eigen for details.
svd	Computes the singular value decomposition of a matrix. See svd for details.
chol backsolve lower.tri	Routines for creating and working with upper and lower triangular factors of matrices. See chol, backsolve, lower.tri, for details.

See Also : Operators

Original Documentation : matrix, cbind, rbind, t, diag, solve, qr, eigen, svd, chol, backsolve, lower.tri

Samples

# Creating a 5 x 4 matrix initialized to 0.0

 m <- matrix(0.0,5,4);
 m
     [,1] [,2] [,3] [,4]
[1,]    0    0    0    0
[2,]    0    0    0    0
[3,]    0    0    0    0
[4,]    0    0    0    0
[5,]    0    0    0    0

# Checking the dimensions

  dim(m)
 [1] 5 4

# Assigning the [5,3] element the value 2.0

  m[5,3] <- 2.0;
  m
     [,1] [,2] [,3] [,4]
[1,]    0    0    0    0
[2,]    0    0    0    0
[3,]    0    0    0    0
[4,]    0    0    0    0
[5,]    0    0    2    0

# Creating a matrix by binding together vectors created
# with the concatenate command.

  M <- rbind(c(0.0,1.0),c(20.0,2.0))
  M
     [,1] [,2]
[1,]    0    1
[2,]   20    2

# Setting up a vector for the right hand side of a matrix equation

  b <- c(0.0,1.0);
  b
 [1] 0 1

# Solving the system of linear equations M x = b 

  solve(M,b);
  [1] 0.05 0.00

UCLA Mathematics Department

©2000