Inner Product Spaces
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Each question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.
In with the standard inner product, compute for and .
Your answer
About these 107 questions
Abstract inner products, norms, orthogonal polynomials, Fourier approximation, and complex Hermitian and unitary matrices. This set covers the chapter Inner Product Spaces in Linear Algebra: 34 easy, 50 medium and 23 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.
- Inner products: the axioms — 9 questions
- Norms, distance, and the norm axioms — 9 questions
- Cauchy–Schwarz and the triangle inequality — 8 questions
- Angles, orthogonality and the Pythagorean theorem — 9 questions
- Orthonormal sets and coordinates — 7 questions
- Gram–Schmidt in a general inner product space — 8 questions
- Orthogonal polynomials: Legendre and Chebyshev — 8 questions
- Orthogonal complements — 7 questions
- Orthogonal projection and best approximation — 9 questions
- Bessel's inequality and Parseval's identity — 7 questions
- Fourier series as orthogonal projection — 9 questions
- Complex inner product spaces — 9 questions
- The adjoint of a linear operator — 8 questions
For work on paper there is a printable problem set with separate worked solutions.