This 13-minute video lesson looks at the determinant when a row is multiplied by a scalar.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

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Conditional Remix & Share Permitted

CC BY-NC-SA
This 13-minute video lesson looks at the determinant when a row is multiplied by a scalar.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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).

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 20-minute video lesson shows how to view the determinant of the transformation matrix as a scaling factor of regions.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 14-minute video lesson shows the proof by induction that transposing a matrix does not change its determinant.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 9-minute video lesson shows how to find the determinant by going along other rows or columns.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 19-minute video lesson provides dot and cross product comparison and Intuition.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 8-minute video lesson looks at the determinant of a matrix with duplicate rows.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This video shows an example using orthogonal change-of-basis matrix to find transformation matrix

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 18-minute video lesson shows how to figure out the formula for a 2x2 matrix. And it defines the determinant.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 13-minute video lesson uses Gram-Schmidt to find an orthonormal basis for a plane in R3.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
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.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 3-minute video lesson looks at the orthogonal complement of the nullspace and left nullspace.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This video shows how to find that the orthogonal complement of the orthogonal complement of V is V

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 22-minute video lesson looks at orthogonal Complements as subspaces.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This video shows that orthogonal matrices preserve angles and lengths

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 16-minute video lesson looks at projections onto subspaces with orthonormal bases.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 17-minute video lesson looks at projections onto subspaces.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Khan, Salman
- Date Added:
- 02/20/2011

Conditional Remix & Share Permitted

CC BY-NC-SA
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.

- Subject:
- Algebra
- Mathematics
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 02/20/2011