This 8-minute video lesson looks at the determinant of a matrix with duplicate rows.

This video shows an example using orthogonal change-of-basis matrix to find transformation matrix

This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.

This 18-minute video lesson shows how to figure out the formula for a 2x2 matrix. And it defines the determinant.

This 13-minute video lesson uses Gram-Schmidt to find an orthonormal basis for a plane in R3.

This 12-minute video lesson looks at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other.

This 3-minute video lesson looks at the orthogonal complement of the nullspace and left nullspace.

This video shows how to find that the orthogonal complement of the orthogonal complement of V is V

This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.

This 27-minute video lesson shows that any member of Rn can be represented as a unique sum of a vector in subspace V and a vector in the orthogonal complement of V.

This 7-minute video lesson gives an alternative (short cut) for calculating 3x3 determinants (Rule of Sarrus).

This 9-minute video lesson shows how to calculate a 4x4 determinant by putting in in upper triangular form first.

This 19-minute video lesson finds an orthonormal basis for a subspace using the Gram-Schmidt Process.

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however.

This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants.

The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.