Khan Academy: Orthogonal Complements: Dim(v) + Dim(orthogonal Complement of V)=n

A video proving that the orthogonal complement of the orthogonal complement of some subspace V must be a member of the original subspace 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 lesson illustrating that the orthogonal complement of the nullspace is equal to the row space and vice versa.

Video builds upon the column spaces and null spaces of the 2x3 matrix and its transpose found in the previous video. Uses them to explain some relationships between the four fundamental subspaces, namely that the orthogonal complement of...

A video lesson figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.

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 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 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...

A video lesson working another example for finding the projection of an arbitrary vector onto a specific subspace in R3. The basis of the subspace is a 3 x 2 matrix. Uses an alternate method for find the transformation matrix that...

Another segment in the series on compound interest and the number e from the Khan Academy. This video begins to derive the formula for interest compounded continuously (A=Pe^rt). Limits are employed to show that the limit of the interest...