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## Matrix Manipulation

This example shows how to do some basic matrix manipulations in MATLAB.

We start by creating a magic square and assigning it to the variable A.

A = magic(3)
A =

8     1     6
3     5     7
4     9     2

Here's how to add 2 to each element of A.

Note that MATLAB requires no special handling of matrix math.

A+2
ans =

10     3     8
5     7     9
6    11     4

The apostrophe symbol denotes the complex conjugate transpose of a matrix.

Here's how to take the transpose of A.

A'
ans =

8     3     4
1     5     9
6     7     2

The symbol * denotes multiplication of matrices.

Let's create a new matrix B and multiply A by B.

B = 2*ones(3)
A*B
B =

2     2     2
2     2     2
2     2     2

ans =

30    30    30
30    30    30
30    30    30

We can also multiply each element of A with its corresponding element of B by using the .* operator.

A.*B
ans =

16     2    12
6    10    14
8    18     4

MATLAB has functions for nearly every type of common matrix calculation. For example, we can find the eigenvalues of A using the "eig" command.

eig(A)
ans =

15.0000
4.8990
-4.8990

This concludes our brief tour of some MATLAB matrix handling capabilities.