If a matrix A has linearly independent columns, then for every vector y there exists a unique least squares solution of .

Name: If a matrix A has linearly independent columns, then for every vector y there exists a unique least squares solution of .
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Question

If a matrix A has linearly independent columns, then for every vector y there exists a unique least squares solution of  .

Quizplus · Accepted Answer

When a matrix has linearly independent columns, it is said to be full rank. A full rank matrix has a unique solution for every vector y in the least squares sense. This solution can be found using the normal equation: 
x = (A^T A)^-1 A^T y.

If a Matrix a Has Linearly Independent Columns, Then for Every