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