R Language Subsetting Elementwise Matrix Operations
Example
Let A and B be two matrices of same dimension. The operators +,-,/,*,^ when used with matrices of same dimension perform the required operations on the corresponding elements of the matrices and return a new matrix of the same dimension. These operations are usually referred to as element-wise operations.
| Operator | A op B | Meaning |
|---|---|---|
| + | A + B | Addition of corresponding elements of A and B |
| - | A - B | Subtracts the elements of B from the corresponding elements of A |
| / | A / B | Divides the elements of A by the corresponding elements of B |
| * | A * B | Multiplies the elements of A by the corresponding elements of B |
| ^ | A^(-1) | For example, gives a matrix whose elements are reciprocals of A |
For "true" matrix multiplication, as seen in Linear Algebra, use %*%. For example, multiplication of A with B is: A %*% B. The dimensional requirements are that the ncol() of A be the same as nrow() of B
Some Functions used with Matrices
| Function | Example | Purpose |
|---|---|---|
| nrow() | nrow(A) | determines the number of rows of A |
| ncol() | ncol(A) | determines the number of columns of A |
| rownames() | rownames(A) | prints out the row names of the matrix A |
| colnames() | colnames(A) | prints out the column names of the matrix A |
| rowMeans() | rowMeans(A) | computes means of each row of the matrix A |
| colMeans() | colMeans(A) | computes means of each column of the matrix A |
| upper.tri() | upper.tri(A) | returns a vector whose elements are the upper |
| triangular matrix of square matrix A | ||
| lower.tri() | lower.tri(A) | returns a vector whose elements are the lower |
| triangular matrix of square matrix A | ||
| det() | det(A) | results in the determinant of the matrix A |
| solve() | solve(A) | results in the inverse of the non-singular matrix A |
| diag() | diag(A) | returns a diagonal matrix whose off-diagnal elemts are zeros and |
| diagonals are the same as that of the square matrix A | ||
| t() | t(A) | returns the the transpose of the matrix A |
| eigen() | eigen(A) | retuens the eigenvalues and eigenvectors of the matrix A |
| is.matrix() | is.matrix(A) | returns TRUE or FALSE depending on whether A is a matrix or not. |
| as.matrix() | as.matrix(x) | creates a matrix out of the vector x |
