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**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

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)

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