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

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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

Conditional Remix & Share Permitted

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

- 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 27-minute video lesson shows that any member of Rn can be represented as a unique sum of a vector in subspace V and a vector in the orthogonal complement of V.

- 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 7-minute video lesson gives an alternative (short cut) for calculating 3x3 determinants (Rule of Sarrus).

- 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 calculate a 4x4 determinant by putting in in upper triangular form first.

- 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 finds an orthonormal basis for a subspace using the Gram-Schmidt Process.

- 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 8-minute video lesson looks at the determinant of an upper triangular 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 9-minute video lesson provides definitions of the vector dot product and vector length.

- 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 19-minute video lesson proves the triangle inequality for vectors in Rn.

- 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 video shows that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n

- 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 19-minute video lesson shows how to define the determinant for nxn matrices. And it provides an exampled of a 4x4 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 14-minute video lesson provides an Introduction to linear transformations.

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