matrix transformations

reflection over the line y = x changes vector from (x over y) to

(y over x)

reflection over the line y = -x changes vector from (x over y) to

(-y over -x)

rotation 90 degrees CCW changes vector from (x over y) to

(-y over x)

rotation 90 degrees CW changes vector from (x over y) to

(y over -x)

reflection across y axis changes vector from (y over x) to

(-x over y)

reflection across x axis changes vector from (y over x) to

(x over -y)

natural projection onto x axis changes vector from (x over y) to

(x over 0)

natural projection onto y axis changes vector from (x over y) to

(0 over y)

if A is an mxn matrix then T(x) defines a transformation

T: R^n → R^m where

• Domain (T) = R^n

• Codomain (T) = R^m

• Range = Column space