A video lesson showing a series of proofs that culminate in explaining that any member of Rn can be represented as a unique sum of a member of some subspace of Rn and a member of its orthogonal complement. Ideas included in the proof are...

Video introducing the orthogonal complement of a subspace and showing that it is also a subspace. Proves that the null space of a matrix is equivalent to the orthogonal complement of its row space by showing that every member of the null...

A video proving that the orthogonal complement of the orthogonal complement of some subspace V must be a member of the original subspace V. Proves that V and the orthogonal complement of the orthogonal complement of V are exactly the...

Video explains what a basis for a vector subspace is and its criteria: the vectors must span the subspace and be linearly independent. Also gives an informal definition of basis as the minimum set of vectors that spans the subspace....

A video lesson showing a series of proofs that culminate in explaining that any member of Rn can be represented as a unique sum of a member of some subspace of Rn and a member of its orthogonal complement. Ideas included in the proof are...

This video 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.

Video introducing the orthogonal complement of a subspace and showing that it is also a subspace. Proves that the null space of a matrix is equivalent to the orthogonal complement of its row space by showing that every member of the null...

A video proving that the orthogonal complement of the orthogonal complement of some subspace V must be a member of the original subspace V. Proves that V and the orthogonal complement of the orthogonal complement of V are exactly the...

A video proving that the orthogonal complement of the orthogonal complement of some subspace V must be a member of the original subspace V.