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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