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 22-minute video lesson looks at orthogonal Complements as subspaces.
This video shows that orthogonal matrices preserve angles and lengths
This 16-minute video lesson looks at projections onto subspaces with orthonormal bases.
This 17-minute video lesson looks at projections onto subspaces.
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.
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 8-minute video lesson looks at the determinant of an upper triangular matrix.
This 9-minute video lesson provides definitions of the vector dot product and vector length.
This 19-minute video lesson proves the triangle inequality for vectors in Rn.
This video shows that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n
This 19-minute video lesson shows how to define the determinant for nxn matrices. And it provides an exampled of a 4x4 determinant.
This 14-minute video lesson provides an Introduction to linear transformations.