# R06 - ENEE 241 02 READING ASSIGNMENT 6 Thu 02/19 Lecture...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ENEE 241 02* READING ASSIGNMENT 6 Thu 02/19 Lecture Topic: cascaded linear transformations; row and column selection; permutation matrices; matrix transpose Textbook References: sections 2.2.3, 2.3 Key Points: • AB represents two linear systems connected in cascade (tandem, series), with system A downstream from system B . • Associativity: ( AB ) C = A ( BC ) def = ABC • Commutativity does not hold in general, i.e., AB 6 = BA . • To select the j th column of a matrix, we right-multiply it by the j th standard unit vector of the appropriate size. To select the i th row of a matrix, we left-multiply it by the i th standard unit vector. • Transposition and multiplication: ( AB ) T = B T A T • A permutation matrix is a square matrix whose columns are distinct standard unit vec- tors. Right-multiplication by a permutation matrix results in column permutation; left- multiplication results in row permutation. • If P is a permutation matrix, then P T P = I (the identity matrix). Thus the inverse of a permutation matrix is its transpose. Theory and Examples: 1 . Viewed as a linear transformation, the product AB represents the cascade (series) connection of B followed by A , as shown below. This means that for a n-dimensional input vector x , the output y is given by...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

R06 - ENEE 241 02 READING ASSIGNMENT 6 Thu 02/19 Lecture...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online