This 13-minute video lesson looks at the determinant when a row is multiplied by a scalar.
This 17-minute video lesson looks at the determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices).
This 22-minute video lesson realizes that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix.
This 20-minute video lesson shows how to view the determinant of the transformation matrix as a scaling factor of regions.
This 14-minute video lesson shows the proof by induction that transposing a matrix does not change its determinant.
This 9-minute video lesson shows how to find the determinant by going along other rows or columns.
This 19-minute video lesson provides dot and cross product comparison and Intuition.
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 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.