Linear Algebra Inner Product Spaces. Students embarking on a linear algebra course should have a thorough knowledge of algebra, and familiarity with analytic geometry and trigonometry. Browse other questions tagged linear-algebra vector-spaces inner-product-space or ask your own question.
x , whose intended interpretation is that it is the length of the vector x.
A nonempty set S ⊂ V of nonzero vectors is called an orthogonal set if all vectors in S are mutually orthogonal.
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Interchanging the two arguments results in the complex conjugate of the original expression Orthogonal sets Let V be an inner product space with an inner product h·, ·i and the induced norm k · k. A vector space that has an inner product defined on it. The norm induced by an inner product is obtained by taking inner-product is a valid norm.
