Orthogonal Complements in Inner Product Spaces | Linear Algebra

We introduce orthogonal complements of subspaces in inner product spaces. We'll see the definition of an orthogonal complement, prove two properties of orthogonal complements, look at an example of finding a basis for an orthogonal complement, and more. If W is a subspace of an inner product space V, the orthogonal complement of W (sometimes read as "W perp") is the set of all vectors in V that are orthogonal to every vector in W. This orthogonal complement is itself a subspace of V. #linearalgebra
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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0:00 Intro
0:28 Definition of Orthogonal Complement
1:27 Orthogonal Complement is a Subspace and W and W Perp have only Zero Vector in Common
2:05 Proof that W Perp is a Subspace
5:50 Proof that W intersect W Perp has only Zero
6:57 Orthogonal Complements come in Pairs
7:58 Finding Orthogonal Complement
10:47 Conclusion
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