MATLAB Operators

What is an Operator?

A specific operation is performed by using a symbol which is called an operator.

Example: A+B, where A, B are called operand and '+' is called operator.

If you want to add any two numbers, we will use the '+' symbol, which is nothing but a plus operator. And if you want to divide any two numbers, we use the '/' symbol, division operator.

MATLAB Operators

MATLAB Operators

In MATLAB, all the operators work both on non-scalar and scalar data. MATLAB offers five categories of operators.

Types of operators:

MATLAB Operators

Arithmetic Operators

Arithmetic operators include functions like summation, multiplication, modulo operations, rounding, power, subtraction, differences and approximate derivatives.

  • +

Symbol= +, corresponding function=plus(), role=Addition

Syntax à C = A+B or C=plus(A,B)

  • +

Symbol= +, corresponding function=uplus(), role=unary plus

Syntax à C = A+B or C=uplus(A,B)

Symbol= -, corresponding function=minus(), role=subtraction

Syntax à C = A-B or C=minus(A,B)

Symbol= -, corresponding function=uminus(), role=unary minus

Syntax à C = A-B or C=uminus(A,B)

  • *

Symbol= *, corresponding function=mtimes(), role=matrix multiplication

Syntaxà C=A*B, here A, B are matrix or C=mtimes(A,B)

  • .*

Symbol= .* , corresponding function=times(), role=element-wise multiplication

Syntax àC=A.*B or C= times(A,B)

  • \

Symbol= \ , corresponding function=mldivide(), role=matrix left division

Syntax à C = A\B or C=mldivide(A,B)

  • .\

Symbol= .\, corresponding function=ldivide(), role=element-wise left division

Syntax à C = A.\B or C=ldivide(A,B)

  • /

Symbol= /, corresponding function=mrdivide(), role=matrix right division

Syntax à C = A/B or C=mrdivide(A,B)

  • ./

Symbol= ./, corresponding function=rdivide(), role=element-wise right division

Syntax à C = A./B or C=rdivide(A,B)

  • ^

Symbol= ^, corresponding function=mpower(), role=matrix power

Syntax àC = A^B or C=mpower(A,B)

  • .^

Symbol=.^ ,corresponding function=power(), role=element-wise power

Syntax àC = A.^B or C = power(A,B)

Symbol=‘  ,corresponding function=ctranspose(), role=complex conjugate transpose

Syntax àB = A’ or B= ctranspose(A)

  • .’

Symbol= .’, corresponding function=transpose(), role=transpose

Syntax àB=A.’ or B = transpose(A)

Example:

We have created a script file which has few of the arithmetic operations implemented.

%arithmetic addition is performed

O = [0 1; 1 0];

C = O + 2

%arithmetic subtraction is performed

A = [2 1; 3 5];

D = A-2

%arithmetic multiplication is performed

q = [1 3 5; 2 4 7];

p = [-5 8  1; 3 9 21; 4 0 8];

f = q*p

%arithmetic division is performed

q1 = [1 1 3; 2 0 4; -1 6 -1];

p1  = [2 19 8];

g = p1/q1

%arithmetic power is performed

q2= [1 2; 3 4];

h = q2^2

%arithmetic transpose is performed

B = [2 1; 9 7; 2 8; 3 5]

J = B'

If we run this above script file we are going to obtain the following output.

Expected Output:

C =

     2     3
     3     2


D =

     0    -1
     1     3


f =

    24    35   104
    30    52   142


g =

    1.0000    2.0000    3.0000


h =

     7    10
    15    22

B =

     2     1
     9     7
     2     8
     3     5


J =

     2     9     2     3
     1     7     8     5

Relational Operators

In MATLAB, Relational operators works on both scalar and non-scalar data. These operators mostly return true or false based on result of operation.

MATLAB Operators
SYMBOLPurpose
==EQUAL TO
~=NOT EQUAL TO
GREATER THAN
>=GREATER THAN OR EQUAL TO
LESS THAN IT
<=LESS THAN OR EQUAL TO

Example:

We have created a script file which has few of the relational operations implemented.

%relational operator "==" is used to check weather matrix q and p are equal

%or not

q = [1+i 3 2 4+i];

p = [1 3+i 2 4+i];

q == p

%Create a duration array and check the condition with relational operator ">=".

f = hours(21:25) + minutes(75)

f >= 1

%Create a array and check the condition with relational operator ">".

w = [1 7 9 11 2 15];

w > 10

%Create array and check the condition with relational operator "<=".

e = [1 7 9 11 2 15];

e <= 12

%Create a array and check the condition with relational operator "<".

d = [1 7 9 11 2 15];

d < 12

%Create g and j arrays, check the condition with relational operator "~=".

g = [1+i 3 2 4+i];

j = [1 3+i 2 4+i];

g ~= j

%Create q1 and p1 matrices to check the condition with relational operator "isequal()".

q1 = zeros(3,3)+1e-20;

p1 = zeros(3,3);

f1 = isequal(q,p1)

If we run this above script file we are going to obtain the following output.

ExpectedOutput:

ans =

  1×4 logical array

   0   0   1   1

f =

  1×5 duration array

   22.25 hr   23.25 hr   24.25 hr   25.25 hr   26.25 hr

ans =

  1×5 logical array

   0   0   1   1   1

ans =

  1×6 logical array

   0   0   0   1   0   1

ans =

  1×6 logical array

   1   1   1   1   1   0

ans =

  1×6 logical array

   1   1   1   1   1   0

ans =

  1×4 logical array

   1   1   0   0

f1 =

logical

   0

 30    52   14

Logical Operators

Onlytwological operators are available in MATLAB.

  1. Element-wise

This type of operator works only on logical arrays.

  
SymbolDescription
&Logical AND
~Logical NOT
|Logical OR
  • Short-circuit

There are two short-circuit logical operators which work on both the operations, scalar and logical.

  
SymbolDescription
||Logical OR (short-circuit)
&&Logical AND (short-circuit)

Example:

We have created a script file which has few of the logical operations implemented.

%And operation of matrix q and p.

q = [5 7 0; 0 2 9; 5 0 0]

p = [6 6 0; 1 3 5; -1 0 0]

q & p

%Logical negation of q.

q1 = eye(3)

p1 = ~q1

%Logical or operations of matrix q and p.

q2 = [5 7 0; 0 2 9; 5 0 0]

p2 = [6 6 0; 1 3 5; -1 0 0]

q2 | p2

%Xor operation of q.

q3 = [true false]

p3 = [true; false]

C = xor(q3,p3)

So, you can simply copy this file and run in your MATLAB software. If we run this above script file we are going to obtain the following output.

Expected output:

q =

     5     7     0

     0     2     9

     5     0     0

p =

     6     6     0

     1     3     5

    -1     0     0

ans =

  3×3 logical array

   1   1   0

   0   1   1

   1   0   0

q1 =

     1     0     0

     0     1     0

     0     0     1

p1 =

  3×3 logical array

   0   1   1

   1   0   1

   1   1   0

q2 =

     5     7     0

     0     2     9

     5     0     0

p2 =

     6     6     0

     1     3     5

    -1     0     0

ans =

  3×3 logical array

   1   1   0

   1   1   1

   1   0   0

q3 =

  1×2 logical array

   1   0

p3 =

  2×1 logical array

   1

   0

C =

  2×2 logical array

   0   1

   1   0

 30    52   14

Bitwise Operators

As the name suggests that these operators work on bit-by-bit operations.

The truth table involved in this operation is as follows.

HKh&kh|kh^k
00000
01011
11110
10011

Various MATLAB bitwise functions are as follows.

  • bitand(g,h)à Bit-wise AND
  • bitor(g,h)à  Bit-wise OR
  • bitcmp(g)à Bit-wise COMPLEMENT
  • bitxor(g,h)à Bit-wise XOR
  • bitget(g,pos)à Bit-wise to get position of a
  • bitset(g,pos)à Bit-wise to set position of a
  • bitShift(g,k)à Bit-wise SHIFT

Let us execute these bitwise functions in MATLAB’s command line and see how itresults.

>>g=34


g =

    34

>>h=7


h =

     7

>>bitand(g,h)


ans =

     2

>>bitor(g,h)


ans =

    39

>bitxor(g,h)


ans =

    37

>>bitcmp(g)


ans =

   1.8447e+19

>>bitget(g,h)


ans =

     0

Set Operations

Set operations include testing set membership, union or intersection of two given sets, it resembles set theory of mathematics.

Various MATLAB set operations are as follows.

  • intersect(A,B)
  • intersect(A,B,’rows’)
  • ismember(A,B)
  • ismember(A,B,’rows’)
  • issorted(A)
  • issorted(A,’rows’)
  • setdiff(A,B)
  • setdiff(A,B,’rows’)
  • setxor(A,B)
  • union(A,B)
  • unique(A)

Let us check out theseset operation functions in MATLAB’s command line.

In the below code, we see two sets: A and B, which are internally created as 1x1 matrix array. We applied all the above-mentioned set operation functions and executed them to get results. The result of each function is reserved in a default variable “ans” created by MATLAB’s environment. Check out the following code.

>>A=[1 6 1 4]


A =

     1     6     1     4

>>B=[8 3 6 3]


B =

     8     3     6     3

>>intersect(A,B)


ans =

     6

>>intersect(A,B,"rows")

ans =

  0×4

>>ismember(A,B)

ans =

  1×4

   0   1   0   0

>>ismember(A,B,"rows")

ans =

logical

   0

>>issorted(A)

ans =

logical

   0

>>issorted(A,'rows')

ans =

logical

   1

>>setdiff(A,B)


ans =

     1     4

>>setdiff(A,B,"rows")


ans =

     1     6     1     4

>>setxor(A,B)


ans =

     1     3     4     8

>>union(A,B)


ans =

     1     3     4     6     8

>>unique(A)


ans =

     1     4     6

 b=7



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