Nonsingular matrix Normal

Nodes, line of, 280 Nondegenerate species (see Species) Nonsingular matrix, 205 Normal coordinates, 19 characters of, 94 degenerate, 93, 107... 

If A is a square matrix and if principal submatrices of A are all nonsingular, then we may choose P as the identity in the preceding factorization and obtain A = LU. This factorization is unique if L is normalized (as assumed previously), so that it has unit elements on the main diagonal. 

The above constitute a set of simultaneous linear algebraic equations, called the normal equations. The matrix X X) is a (/ x k) symmetric matrix. Assumption 4 made earlier guarantees that (X X) is nonsingular therefore, its inverse exists. Thus, the normal equations can be solved for the vector b ... 

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