:The articles on Determinant, Invertible matrix, Identity matrix, and Matrix multiplication look nice, and link to other stuff.
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If the Hessian is close to a non-invertible matrix, the inverted Hessian can be numerically unstable and the solution may diverge.
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*For any real invertible matrix A, the product A ^ { \ mathrm { T } } A is a positive definite matrix.
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In the case of a linear system which is underdetermined, or an otherwise non-invertible matrix, singular value decomposition ( SVD ) is equally useful.
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With the unusually large key is an invertible matrix used to encrypt the session keys, and the encrypted session keys must be sent along with the ciphertext.
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Can an invertible matrix Q be found such that both Q ^ {-1 } A Q and Q ^ {-1 } B Q are diagonal matrices?
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:I think the solution would involve showing that the matrix formation of the equation that gives you your best fit curves involves an invertible matrix, and from that has a unique solution.
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Then the first part of the algorithm computes an LU decomposition, while the second part writes the original matrix as the product of a uniquely determined invertible matrix and a uniquely determined reduced row echelon matrix.
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For example, Jordan normal form is a canonical form for matrix similarity, and the row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix.
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If a square, invertible matrix has an " LDU " factorization with all diagonal entries of " L " and " U " equal to 1, then the factorization is unique.
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