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Page 1: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 2: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 3: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 4: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard

Inner product

Page 5: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 6: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 7: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 8: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 9: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard

The angle between vectors x and y:

Page 10: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 11: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 12: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard

Transformations by orthogonal matrices are special because the length of a vector x is not changed when transforming it using an orthogonal matrix A, not the inner product between vectors x and y.

Page 13: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 14: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 15: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 16: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard
Page 17: Donald Bren School of Information and Computer Sciences ...vector in U. Furthermore, U n UL = {0} so that any vector e V can be Example 3.8 (Orthonormal Basis) The canonical/standard

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