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Cartoon Plane, Multiview Projection, Orthographic Projection, Projection, Angle, Drawing, Perspective, Technical Drawing, Multiview Projection, Projection, Orthographic Projection png 1181x1024px 120.62KB. Linear subspace Linear algebra space Linear map System of linear equations, a linear design, angle, rectangle, triangle png 1441x1441px 185.08KB. Black and white Line Angle Point, Paper shadow projection angle, texture, white, rectangle png 1200x700px 20.62KB. Linear span space Linear map Linear algebra, Euclidean, angle, rectangle, triangle png 1024x1024px 80.41KB. space Linear subspace Linear algebra, linear, angle, rectangle, triangle png 800x564px 58.02KB. We denote the closest vector to x on W by x W. Let W be a subspace of R n and let x be a vector in R n. Subsection 6.3.1 Orthogonal Decomposition This is exactly what we will use to almost solve matrix equations, as discussed in the introduction to Chapter 6. The vector x W is called the orthogonal projection of x onto W. In this section, we will learn to compute the closest vector x W to x in W. 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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