Inner Product Spaces
Orthogonality, projections, Gram-Schmidt, and adjoint operators.
Inner Product Spaces. Orthogonality, projections, Gram-Schmidt, and adjoint operators. This page collects canonical references that organise the subject and provide entry points to its main techniques.
Foundations and canonical references
The standard treatments of inner product spaces approach the subject from complementary angles. Axler, Linear Algebra Done Right (2015) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Halmos, Finite-Dimensional Vector Spaces (1974) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for inner product spaces include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2015Linear Algebra Done Rightaxler-2015
- textbook · supporting · 1974Finite-Dimensional Vector Spaceshalmos-1974
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