Let W be a subspace of R n and let x be a vector in R n. Vocabulary words: orthogonal decomposition, orthogonal projection.Pictures: orthogonal decomposition, orthogonal projection.Recipes: orthogonal projection onto a line, orthogonal decomposition by solving a system of equations, orthogonal projection via a complicated matrix product.Learn the basic properties of orthogonal projections as linear transformations and as matrix transformations.Understand the relationship between orthogonal decomposition and the closest vector on / distance to a subspace.Understand the relationship between orthogonal decomposition and orthogonal projection.Understand the orthogonal decomposition of a vector with respect to a subspace.Section 6.3 Orthogonal Projection ¶ Objectives Hints and Solutions to Selected Exercises.
3 Linear Transformations and Matrix Algebra
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