This art history video presents a conversation between Salman Khan and Beth Harris about Leonardo da Vinci's "Mona Lisa" (c. 1503-1505, oil on panel) and its changing meaning. (Musée du Louvre).

This 16-minute video lesson shows that a projection onto a subspace is a linear transformation. [Linear Algebra playlist: Lesson 110 of 143]

This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.

This 25-minute video lesson introduces the idea of an angle between two vectors.

This 27-minute video lesson provides an example using the orthogonal change-of-basis matrix to find the transformation matrix. [Linear Algebra playlist: Lesson 128 of 143]

This 17-minute video lesson shows how to express a projection on to a line as a Matrix Vector prod. [Linear Algebra playlist: Lesson 61 of 143]

This 15-minute video lesson shows how to find the eigenvectors and eigenspaces of a 2x2 matrix. [Linear Algebra playlist: Lesson 136 of 143]

This 12-minute video lesson provides an introduction to the null space of a matrix and shows that the null space of a matrix is a valid subspace. [Linear Algebra playlist: Lesson 34 of 143]

This 18-minute video lesson shows how to solve a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 30 of 143]

This 12-minute video lesson provides another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 32 of 143]

This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]

This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]

This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]

This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]

This 12-minute video lesson finds that the orthogonal complement of the orthogonal complement of V is V. [Linear Algebra playlist: Lesson 103 of 143]

This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]

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

This 23-minute video lesson looks at Rowspace and Left Nullspace. [Linear Algebra playlist: Lesson 97 of 143]