Matrix Teacher Resources

A video showing how any linear transformation can be represented as a matrix vector product.

A video lesson figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.

This video shows that the sum of two transformations is equal to the sum of their transformation matrices. Defines scalar multiples of linear transformations and shows that they are equal to the scalar multiples of their transformation...

This video uses a concrete example for how to find the projection of an arbitrary vector onto a specific subspace in R4. Uses a 4 x 2 basis matrix for the subspace.

Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set.

Video first reviews the closure properties of subspaces. Shows that the image of a subspace under a linear transformation is a subspace. Connects the meaning of range to the image of the transformation. Shows that the image of the linear...

Video first reviews the closure properties of subspaces. Shows that the image of a subspace under a linear transformation is a subspace. Connects the meaning of range to the image of the transformation. Shows that the image of the linear...

Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the co-domain.

Expressing a Projection on to a line as a Matrix Vector prod

Video shows how to write a transformation matrix in R^3 that rotates a vector around the x-axis. Compares the rotation matrix in R^3 to the rotation matrix in R^2 found in the previous video and discusses how it could be applied for more...

Creating scaling and reflection transformation matrices (which are diagonal).

Showing that (transpose of A)(A) is invertible if A has linearly independent columns in this short video.

Showing that inverse transformations are also linear.

A video lesson explaining that a transformation matrix is invertible if and only if it is a square identity matrix in reduced row echelon form.

An instructional video that explains how the method for finding the inverse transformation matrix is derived. It is the same method for finding the inverse for any invertible matrix. [18:00]

A video lesson explaining that a transformation matrix is invertible if and only if it is a square identity matrix in reduced row echelon form. This video is also found in the strand Algebra: Matrices. [6:37]

Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram. Includes...

A video lesson that gives an in-depth, algebraic proof showing that the inverse of a linear transformation is also linear. [21:25]

Video creating a basis out of n linearly independent eigenvectors. Reviews transformations and change of basis matrices. Shows that when the eigenbasis is used as an alternate coordinate system, the transformation is a diagonal matrix...

Video first graphs the transformation image of a specific transformation. Then examines the solution set for a couple particular points in the image. Shows that the solution set is a shifted version of the null space. [16:34]

Video creating a basis out of n linearly independent eigenvectors. Reviews transformations and change of basis matrices. Shows that when the eigenbasis is used as an alternate coordinate system, the transformation is a diagonal matrix...

Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram.

College-level course highlighting the biology of cells of higher organisms. Course topics include cellular membranes and organelles; cell growth and oncogenic transformation; transport, receptors, and cell signaling; the cytoskeleton,...

Come to this site to find the transformational matrix to find the vector rotated 90 degrees from the original. The site also states the special relationship between two perpendicular vectors when using the dot product.