Tempest Desh said:Homework Statement
Find the orthogonal complement.
Homework Equations
span {[0 0 1 0] [2 -1 0 1]} transpose
The Attempt at a Solution
I'm really confused on this. I've tried setting up things like this:
[0 0 1 0] [2 -1 0 1] [x y z v] transpose = [0 0 0 0] transpose
But, I'm not sure where to go from here...all the examples I see having two column matrices...not split up like in this problem...
The orthogonal complement of a vector space is the set of all vectors that are perpendicular (or orthogonal) to every vector in that space.
The orthogonal complement is often denoted as the symbol ⊥ or with a superscript ⊥, placed above the vector space symbol.
The orthogonal complement is a subspace of the vector space, and together they form a direct sum. This means that every vector in the vector space can be written as a unique combination of a vector in the orthogonal complement and a vector in the original space.
Yes, the concept of orthogonal complement can be extended to non-Euclidean spaces, such as spaces with a non-trivial metric. However, the definition and properties may differ from those in Euclidean spaces.
The orthogonal complement is useful in various applications, such as in linear algebra, signal processing, and optimization problems. It allows for the decomposition of a vector space into two independent subspaces, making it easier to solve problems and analyze data.