If
is a linear dependent set of nonzero vectors in a vector space V, and
is any inner product on V, then there exists
such that

.

Name: If is a linear dependent set of nonzero vectors in a vector space V, and is any inner product on V, then there exists such that .
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Question

If 
  is a linear dependent set of nonzero vectors in a vector space V, and 
  is any inner product on V, then there exists 
  such that 
  
.

Quizplus · Accepted Answer

This is true by the Gram-Schmidt orthogonalization process. We can apply the process to the linearly dependent set of vectors and obtain an orthonormal basis with respect to the given inner product.

If Is a Linear Dependent Set of Nonzero Vectors