When performing basic arithmetic operations on matrices, use the standard arithmetic operators. For example, add, subtract, multiply, and divide the following two matrices by using the standard +, -, *, and / operators:
A := matrix([[a, b], [c, d]]): B := matrix([[1, 2], [3, 4]]): A + B, A - B, A*B, A/B
To perform basic operations on a matrix and a number, use the same operators. When you multiply a matrix by a number, MuPAD^{®} multiplies all elements of a matrix by that number:
5*A
When you add a number to a matrix, MuPAD multiplies the number by an identity matrix, and then adds the result to the original matrix:
A + 5
Note: MATLAB^{®} adds a number to each element of a matrix. MuPAD adds a number only to the diagonal elements of a matrix. |
You can combine matrices with the same number of rows by using
the concatenation operator (.
):
A.B
Besides standard arithmetic operations, many other MuPAD functions are available for computations involving matrices and vectors. To check whether a particular function accepts matrices as parameters, see the "Parameters" section of the function help page. The following functions can operate on matrices:
The conjugate
function
computes the conjugate of each complex element of a matrix:
A := matrix([[1, 2 + 3*I], [1 - I, 2*I]]): conjugate(A)
The int
and diff
functions compute
the derivative and the integral of each element of a matrix:
A := matrix(2, 2, [x, x^2, x^3, x^4]): int(A, x), diff(A, x)
The expand
function
expands each element of a matrix:
A := matrix(2, 2, [x, (x + 1)^2, x*(x - 1), x*(x + 4)]): expand(A)
The map
function
applies the specified function to all operands of each element of
a matrix:
A := matrix(3, 3, [1, 2, 3], Diagonal): B := map(A, sin)
The float
function
converts each element of a matrix or numerical subexpressions of each
element of a matrix to floating-point numbers:
float(B)
The evalAt
function (and its shortcut |
) substitutes
the specified object by another specified object, and then evaluates
each element of a matrix:
A := matrix(2, 2, [x, x^2, x^3, x^4]): A|x = 2
The subs
function
returns a copy of a matrix in which the specified object replaces
all instances of another specified object. The function does not evaluate
the elements of a matrix after substitution:
A := matrix(2, 2, [x, x^2, x^3, x^4]): subs(A, x = exp(y))
The has
function
determines whether a matrix contains the specified object:
A := matrix(2, 2, [x, x^2, x^3, x^4]): has(A, x^3), has(A, x^5)
The iszero
function
checks whether all elements of a matrix are zeros:
A := matrix(2, 2): iszero(A)
A[1, 1] := 1: iszero(A)
The norm
function
computes the infinity norm (row sum norm) of a matrix:
A := matrix(2, 2, [a_1_1, a_1_2, a_2_1, a_2_2]): norm(A)
The zip(A, B, f)
function combines
matrices A
and B
into a matrix C
so
that C_{ij} = f(A_{ij}, B_{ij}):
A := matrix(2, 2, [a, b, c, d]): B := matrix(2, 2, [10, 20, 30, 40]): zip(A, B, _power)