Last revised 28 OCT 2010, by JMB
Maybe you really want the index page instead.
All these notes are available in both DVI and PDF formats.
Notes for 110.201 Linear Algebra
Linear Substitutions and Matrix Multiplication (2 pages)
Matrix multiplication is explained by an example in terms of composition
of linear substitutions. This context leads naturally to the associative
law and the identity and zero matrices. Available in your choice of:
Inverse Linear Substitutions and Matrices (1 page)
The inverse of a matrix is explained by an example in terms of solving
a linear system, or equivalently as row reduction applied to the augmented
matrix [A|I]. Available in your choice of:
Inverting 2x2 Matrices (2 pages) The generic 2x2 matrix
is inverted using only standard row reduction techniques, without recourse
to guesswork or ingenuity. Available in your choice of:
Coordinate Vectors (2 pages) A basis B of a
general vector space V is described as a method of identifying
V with euclidean n-space. This leads to the formula for
the effect of a change of basis on coordinate vectors. When V is
an inner product space, one sees why B should be chosen orthonormal.
Available in your choice of
Row Space and Column Space (2 pages) A worked example
computes the null space, row space, rank and column space of a 4x5 matrix
A. Available in your choice of:
Linear Transformations and Matrices (2 pages) Given bases
of vector spaces V and W, the matrix of a general linear
transformation from V to W is obtained. Composition of linear
transformations corresponds to matrix multiplication. The formula for
change of bases is deduced. Available in your choice of:
Diagonalization (2 pages) This discusses the effect of
using a non-standard basis on the matrix of a linear transformation from
euclidean n-space to itself. The matrix is diagonalizable if a
basis of eigenvectors exists. Available in your choice of: