Linear Algebra · Algebra
Inner Product Spaces and Orthogonality
An inner product gives a vector space geometry. The Spectral Theorem says every symmetric matrix has an orthonormal eigenbasis — a fact central to statistics, physics, and data analysis.
WHAT STUDENTS WILL LEARN
✓Define inner products and induced norms
✓Apply Gram-Schmidt orthogonalization
✓Use orthogonal projections and least squares
✓Apply the Spectral Theorem for symmetric matrices
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