MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.
MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.
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)