UNIT 3

Matrices and Transformation

Chapter 9 & 14

A Matrix is an array of numbers:

 

Types of matrices

1. Row matrix: has only one row

2. Column matrix: has only one column

3.  Rectangular matrix: rows and columns are not equal

4. Square matrix: Rows and columns are equal

5. Diagonal matrix: at least one elements of principal diagonal is non-zero and the rest are zero

6. Scalar matrix: all the elements in the diagonal are same

7. Identity or unit matrix: diagonal elements equal to one, denoted by I

8. Triangular matrix: all elements below principal diagonal are zero or all the elements above                                                  principal diagonal are zero

9. Null/Zero matrix: all the elements are zero

Adding

These are the calculations:

3+4=7	8+0=8
4+1=5	6-9=-3

The two matrices must be the same size, i.e. the rows must match in size, and the columns must match in size.

Negative

These are the calculations:

-(2)=-2	-(-4)=+4
-(7)=-7	-(10)=-10

Subtracting

These are the calculations:

3-4=-1	8-0=8
4-1=3	6-(-9)=15

Multiply by a Constant

These are the calculations:

2×4=8	2×0=0
2×1=2	2×-9=-18

*scalar multiplication

Multiplying a matrix to other matrix

                          

Dividing

A/B = A × (1/B) = A × B^-1

where B^-1 means the "inverse" of B.

So we don't divide, we multiply by an inverse.

Inverse

Transposing

To "transpose" a matrix, swap the rows and columns.