The usual mathematical operators ( eg. +, -, *, / ) operate on
matrices as well as scalars. Lets look at the various binary operations,
for A binop B:
- +
- Does element-by-element addition of two matrices.
The row and column dimensions of
A and
B must be the same, unless either A or
B is a 1-by-1 matrix; in this case a
scalar-matrix addition operation is performed.
- –
- Does element-by-element subtraction of two matrices.
The row and column dimensions of both
A and
B must be the same, unless either A or
B is a 1-by-1 matrix; in this case a
scalar-matrix subtraction operation is performed.
- *
- Performs matrix multiplication on the two
operands. The column dimension of
A must match
the row dimension of B, unless either A or
B is a 1-by-1 matrix; in this case a
scalar-matrix multiplication is performed.
- /
- Performs matrix ``right-division'' on it's operands.
The matrix right-division (
A/B) can be thought of
as A*inv (B). The column dimensions of A
and B must be the same. Internally right division
is the same as ``left-division'' with the arguments
transposed.
A/
B = (
BT 
AT)
T
The exception to this dimension rule
occurs when B is a 1-by-1 matrix; in this case a
matrix-scalar divide occurs.
Additionally, has several other operators that function on
matrix operand(s).
- .*
- Performs element-by-element multiplication on
it's operands. The operands must have the same row and
column dimensions, unless either
A or B is
a 1-by-1 matrix.
- ./
- Performs element-by-element division on it's
operands. The operands must have the same row and column
dimensions, unless either
A or B is a
1-by-1 matrix.
- Performs matrix ``left-division''. Given
operands
A\B, matrix left division is the
solution to the set of equations Ax = B. If B has
several columns, then each column of x is a solution
to A*x[;i] = B[;i]. The row dimensions of
A and B must agree.
-
.
- Performs element-by-element left-division.
Element-by-element left-division is provided for
symmetry, and is equivalent to
B./A. The row and
column dimensions of A and B must agree,
unless either one is a 1-by-1 matrix.
-
∧
A^B raises A to the B
power. When A is a matrix, and B is an
integer scalar, the operation is performed by successive
multiplications. When B is not an integer, then
the operation is performed using A's eigenvalues
and eigenvectors. The operation is not allowed if
B is a matrix.
-
.∧
A.^B raises A to the
B power in an element-by-element fashion. Either
A or B can be matrix or scalar. If both
A and B are matrices, then the row and
column dimensions must agree.
- '
- This unary operator performs the matrix transpose
operation.
A' swaps the rows and columns of A.
For a matrix with complex elements a complex conjugate
transpose is performed.
- .'
- This unary operator performs the matrix
transpose operation.
A.' swaps the rows and
columns of A. The difference between ' and
.' is only apparent when A is a complex
matrix; then A.' does not perform a complex
conjugate transpose.
There are several details that are very important to note:
- The operators that are denoted by two symbol should not
have any white space or any other character between the
two symbols.
- The expression
2./A is not interpreted as
2. /A. is smart enough to group the period with
the /.