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Chapter 7 Orthogonality
After completing this chapter, students should be able to do the following.
Objectives
Compute the dot product of two vectors, and understand the geometric interpretation of the dot product.
Define orthogonality in the context of vectors.
Discuss orthogonal and orthonormal bases, Gram-Schmidt orthogonalization, orthogonal complements, and projections.
Explain how orthogonal projections relate to least square approximations.
Discuss general inner product spaces and symmetric matrices, and associated norms.
Discuss the singular value decomposition of a matrix.
