Eigenvalues of A and

Thus each eigenvalue of is an eigenvalue of A and vice versa. In this case the matrices A and are said to be similar and T is called similarity transformation. 

Determinants and Eigenvalues of A and D Several molecular descriptors are defined from determinants or eigenvalues of A, D, and A + D. The interested reader is referred elsewhere [20,21],... 

A trace criterion for precise estimation was introduced by Pinto, Lobao, and Monteiro (1990). Here one selects the next experiment to minimize A , the trace of the inverse matrix A . This quantity is the sum of the eigenvalues of A and is proportional to the sum of the variances... 

Other useful properties are that if A and B share an eigenvector, then both AB and BA will also share that eigenvector, and the corresponding eigenvalue of the product will just be the product of the eigenvalues of A and B. The square root cannot be larger than the larger of these factors. 

The matrices P and Q are both unit lower triangular matrices. The non-diagonal entries of -F1 in P are in identical positions to the corresponding non-diagonal entries of — I in Q. Therefore, by the standard rules of matrix multiplication. PQ = I and Q = P . Note the appearance of off-diagonal -t-l entries in P in the same places as the off-diagonal — 1 entries in Q is a strict requirement for PQ = I and therefore for equivalence of the eigenvalues of A" and A. 

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