Math> Linear algebra> Vectors and spaces> Subspaces and the basis for a subspace © 2025 Khan Academy

Math> Linear algebra> Vectors and spaces> Subspaces and the basis for a subspace © 2025 Khan Academy

Subspaces and the basis for a subspace Learn Linear subspaces Basis of a subspace

This was a projection onto a line. Notice when we're dealing with an orthonormal basis for a subspace, when you take a projection of any vector in Rn onto that subspace, it's essentially, …

Gram-Schmidt example with 3 basis vectorsI am puzzled. Is this not an example of computing in a unnecessarily complicated way? If we pick the order of vectors to be ortonormalized in a …

Which is pretty interesting. So if I have this set, this orthonormal set right here, it's also a set of linearly independent vectors, so it can be a basis for a subspace. So let's say that B is the …

Finding an orthonormal basis for a subspace using the Gram-Schmidt Process. Created by Sal Khan.

Unit 1: Vectors and spaces Vectors Linear combinations and spans Linear dependence and independence Subspaces and the basis for a subspace Vector dot and cross products …

Dimension of the Null Space or NullityI am confused. In a previous video ("null space and column space") we learned that the "basis" are the column vectors that correspond to the pivot entries …

Using Gram-Schmidt to find an orthonormal basis for a plane in R3