>> A matrix is a two-dimensional array of numbers. Vectors are special cases of matrices having one row or one column.
>> 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:
>> If the matrix is small you can type it row by row, separating the elements in a given row with spaces or commas and separating the rows with semicolons. For example, typing
A = [2,4,10;16,3,7];
Remember, spaces or commas separate elements in different columns, whereas semicolons separate elements in different rows.
>> To create matrices from Vectors suppose a = [1,3,5] and b = [7,9,11] (row vectors). Note the difference between the results given by [a b] and [a;b] in the following session:
You need not use symbols to create a new array. For example, you can type
D = [[1,3,5];[7,9,11]];
Referencing the Elements of a Matrix:
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:
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:
You can also select the elements in the mth through nth columns, for this we write:
a(:,m:n)
In the same way, you can create a sub-matrix taking a sub-part of a matrix.
n 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:
Array addressing:
The colon operator selects individual elements, rows, columns, or ''subarrays'' of arrays. Here are some examples:
v(:) = represents all the row or column elements of the vector v.
v(2:5) = represents the second through fifth elements; that is v(2), v(3), v(4), v(5).
A(:,3) = denotes all the elements in the third column of the matrix A.
A(:,2:5) = denotes all the elements in the second through fifth columns of A.
A(2:3,1:3) = denotes all the elements in the second and third rows that are also in the first through third columns.
Examples:
Try these operation yourself.
>> a= [4 5 6; 1 2 3; 7 8 9]
>> a(:)
>> a= [4 5 6; 1 2 3; 7 8 9]
>> a(2:5)
>> a(: , 3)
>> a= [4 5 6; 1 2 3; 7 8 9]
>> a(: , 2:3)
>> a(: , 2:5)
Output…….?
Deleting a Row or a Column in a Matrix:
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:
Next, let us delete the fifth column of a:
Example:
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.
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