Matrix Representation of Transformations

Represent

points and vectors as matrices. In 2D,

This is a Shorthand:

Coordinates are specified relative to a frame :

Technically,

• Should write the as .
• The frame F should note what space it's in.

Usually,

we're lazy and let ' ' denote both

• The point
• Its matrix representation relative to an understood frame.

Transformations:

• is the frame of the domain,
• is the frame of the range.

Then ...

transforms to .

Can also read this as .

is said to be the matrix representation of T relative to and .

• First column of is representation of in .
• Second column of is representation of in .
• Third column of is representation of in .