A video lesson explaining how to change from coordinates with respect to a given basis to traditional Cartesian coordinates and vice versa by using a change of basis matrix. Includes concrete examples in R3. [17:55]

Video uses the vector triangle inequality and the law of cosines to demonstrate and prove the definition of the angle between vectors. Uses the definition of the angle between vectors to define perpendicular vectors. Shows that the dot...

A video lesson defining projections onto subspaces. Uses the definition for a projection onto a line and then shows that a generalized version of the formula works for a projection onto any subspace. Includes a concrete example and...

Video solving for the shortest distance between a point and a plane by building from the previous video where the normal vector to the plane is found. Distance is calculated by finding the dot product of the vector from the given point...

A video lesson explaining how to convert between traditional Cartesian coordinates and coordinates with respect to a given basis by using an invertible change of basis matrix. Includes two concrete examples in R2. [13:34]

Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...

Video gives an intuition of what dot product and cross product represent. Also gives a comparison between cross product and dot product of vectors and how they are related. Shows which angles maximize the cross product and dot product....

A video lesson showing that vectors in space can be defined by coordinates with respect to a basis. A concrete example is given for a vector in R2. Shows how the vector is defined in traditional Cartesian coordinates and then how it can...

A video lesson showing what a projection onto a plane could look like. Illustrates that the newly derived definition of a projection holds true for projections onto subspaces other than lines. [9:27]

Demonstrates how to find the appropriate combination of two given vectors in order to obtain a third given vector. This is done by representing the problem with a single matrix equation and solving that equation. [14:20]

Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...

Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors.

Video gives an intuition of what dot product and cross product represent. Also gives a comparison between cross product and dot product of vectors and how they are related. Shows which angles maximize the cross product and dot product....

This video gives an intuition of what dot product and cross product represent. Also gives a comparison between cross product and dot product of vectors and how they are related.