Composing and Inverting Transformations
One of the main motivations for using matrices to represent linear transformations is that transformations can then be easily composed (combined) and inverted.
Composition is accomplished by matrix multiplication. If A and B are the matrices of two linear transformations, then the effect of applying first A and then B to a vector x is given by:
(This is called the Associative property.) In other words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices. Note that the multiplication is done in the opposite order from the English sentence: the matrix of "A followed by B" is BA, not AB.
A consequence of the ability to compose transformations by multiplying their matrices is that transformations can also be inverted by simply inverting their matrices. So, A-1 represents the transformation that "undoes" A.
Read more about this topic: Transformation Matrix
Famous quotes containing the word composing:
“If I had my life over again I should form the habit of nightly composing myself to thoughts of death. I would practise, as it were, the remembrance of death. There is no other practice which so intensifies life. Death, when it approaches, ought not to take one by surprise. It should be part of the full expectancy of life. Without an ever- present sense of death life is insipid. You might as well live on the whites of eggs.”
—Muriel Spark (b. 1918)