MATLAB - Matrix

A matrix is a two-dimensional array of numbers.
In MATLAB, you create a matrix by entering elements in each row as comma or space delimited numbers and using semicolons to mark the end of each row.
For example, let us create a 4-by-5 matrix a −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]
MATLAB will execute the above statement and return the following result −
a =
      1     2     3     4     5
      2     3     4     5     6
      3     4     5     6     7
      4     5     6     7     8

To reference an element in the mth row and nth column, of a matrix mx, we write −
mx(m, n);

For example, to refer to the element in the 2nd row and 5th column, of the matrix a, as created in the last section, we type −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(2,5)
MATLAB will execute the above statement and return the following result −
ans =  6

To reference all the elements in the mth column we type A(:,m).
Let us create a column vector v, from the elements of the 4th row of the matrix a −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
v = a(:,4)
MATLAB will execute the above statement and return the following result −
v =
      4
      5
      6
      7

You can also select the elements in the mth through nth columns, for this we write −
a(:,m:n)
Let us create a smaller matrix taking the elements from the second and third columns −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(:, 2:3)
MATLAB will execute the above statement and return the following result −
ans =
      2     3
      3     4
      4     5
      5     6

In the same way, you can create a sub-matrix taking a sub-part of a matrix.
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(:, 2:3)
MATLAB will execute the above statement and return the following result −
ans =
      2     3
      3     4
      4     5
      5     6

In the same way, you can create a sub-matrix taking a sub-part of a matrix.
For example, let us create a sub-matrix sa taking the inner subpart of a −
3     4     5     
4     5     6     

To do this, write −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
sa = a(2:3,2:4)
MATLAB will execute the above statement and return the following result −
sa =
      3     4     5
      4     5     6

You can delete an entire row or column of a matrix by assigning an empty set of square braces [] to that row or column. Basically, [] denotes an empty array.
For example, let us delete the fourth row of a −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a( 4 , : ) = []
MATLAB will execute the above statement and return the following result −
a =
      1     2     3     4     5
      2     3     4     5     6
      3     4     5     6     7

Next, let us delete the fifth column of a −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(: , 5)=[]
MATLAB will execute the above statement and return the following result −
a =
      1     2     3     4
      2     3     4     5
      3     4     5     6
      4     5     6     7

In this example, let us create a 3-by-3 matrix m, then we will copy the second and third rows of this matrix twice to create a 4-by-3 matrix.
Create a script file with the following code −
a = [ 1 2 3 ; 4 5 6; 7 8 9];
new_mat = a([2,3,2,3],:)
When you run the file, it displays the following result −
new_mat =
      4     5     6
      7     8     9
      4     5     6
      7     8     9

In this section, let us discuss the following basic and commonly used matrix operations −
Addition and Subtraction of Matrices
Addition and Subtraction of Matrices
Division of Matrices
Division of Matrices
Scalar Operations of Matrices
Scalar Operations of Matrices
Transpose of a Matrix
Transpose of a Matrix
Concatenating Matrices 
Concatenating Matrices 
Matrix Multiplication
Matrix Multiplication
Determinant of a Matrix
Determinant of a Matrix
Inverse of a Matrix
Inverse of a Matrix

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