Section 1.8:
Part 1- Standard basis vectors for Rn.
Part 2- Linear Transformations from Rn to Rm and linear operators from Rn to Rn. Functions, image, domain, codomain and range. Standard matrix, multiplication by A and linearity properties. Finding the standard matix of a linear transformation.
Pages 82-83: 1-24, 27, 28, 29, 31
Notes to be added to your textbook
Section 4.9: Geometry of linear transformations. Zero transformation and identity operator. Reflection, projection, rotation, dilation and contraction operators.
Pages 268-270: 1-16, 21a , 22 a, 23 a, 29, 30, 31, 32, 40 a
Section 4.10: Properties of linear transformations from Rn to Rm. Compositions of linear transformations. One to one linear transformations. Inverse operator. Finding the standard matrix of inverse operators.
Pages 278-279: 1-20, 21, 22, 31 a, 32 a, 33
Section 5.1: Eigenvalues & Eigenvectors.
Eigenvector of A, eigenvalue of A, characteristic equation, characteristic polynomial of A. Eigenvalues of
triangular matrices. Eigenvalues of the powers of a matrix. Eigenvalues and invertibility.
Pages 300-302: 1-14
Liliana Menjivar
Instructor