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# Orthonormal bases.

Definition 12.4.1   Let be a basis for the vector space . If , the basis is called an orthogonal basis for .

Definition 12.4.2   An orthonormal basis of the vector space is an orthogonal basis, all of whose vectors being unit vectors.

This means that in an orthonormal basis, the vectors are orthogonal and of length 1.

Example 12.4.3   Some orthonormal bases for :
• .
• .