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

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Algebra
Mathematics
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Author:
Khan, Salman
02/20/2011
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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.

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Algebra
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Author:
Khan, Salman
02/20/2011
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This 3-minute video lesson looks at the orthogonal complement of the nullspace and left nullspace.

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Algebra
Mathematics
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Author:
Khan, Salman
02/20/2011
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This video shows how to find that the orthogonal complement of the orthogonal complement of V is V

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02/20/2011
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This 22-minute video lesson looks at orthogonal Complements as subspaces.

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Algebra
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Khan, Salman
02/20/2011
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This video shows that orthogonal matrices preserve angles and lengths

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02/20/2011
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This 16-minute video lesson looks at projections onto subspaces with orthonormal bases.

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Algebra
Mathematics
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Author:
Khan, Salman
02/20/2011
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This 17-minute video lesson looks at projections onto subspaces.

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Algebra
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Author:
Khan, Salman
02/20/2011
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This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.

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Algebra
Mathematics
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Author:
Salman Khan
02/20/2011
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This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.

Subject:
Algebra
Mathematics
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Author:
Salman Khan
02/20/2011
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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.

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Algebra
Mathematics
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Author:
Khan, Salman
02/20/2011
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This 7-minute video lesson gives an alternative (short cut) for calculating 3x3 determinants (Rule of Sarrus).

Subject:
Algebra
Mathematics
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Author:
Khan, Salman
02/20/2011
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This 9-minute video lesson shows how to calculate a 4x4 determinant by putting in in upper triangular form first.

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Algebra
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Author:
Khan, Salman
02/20/2011
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This 19-minute video lesson finds an orthonormal basis for a subspace using the Gram-Schmidt Process.

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Algebra
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Author:
Khan, Salman
02/20/2011
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This 8-minute video lesson looks at the determinant of an upper triangular matrix.

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Algebra
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Author:
Khan, Salman
02/20/2011
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This 9-minute video lesson provides definitions of the vector dot product and vector length.

Subject:
Algebra
Mathematics
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Author:
Salman Khan
02/20/2011
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This 19-minute video lesson proves the triangle inequality for vectors in Rn.

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Algebra
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Author:
Salman Khan
02/20/2011
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This video shows that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n

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Algebra
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02/20/2011
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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
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Author:
Khan, Salman
02/20/2011
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This 14-minute video lesson provides an Introduction to linear transformations.

Subject:
Algebra
Mathematics
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