On the Matric Equation TA = BT + C

Ingraham, Mark H.; Trimble, H. C.

doi:10.2307/2371272

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Is a Solution Ofeaix { = 0 If And Only If\i-xisa Right Fac1

Tensor Equations1

If X Is a Solution Ofeaix^o Then The Determinant Of The Mat1

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1941

2006

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Cited by 3 publications

(3 citation statements)

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“…Theorem 5, which is a corollary of a theorem due to Phillips,8 yields us an algorithm better than the W.P.A. This theorem is as follows : THEOREM …”

Section: Is a Solution Ofeaix { = 0 If And Only If\i-xisa Right Facmentioning

confidence: 95%

“…That these conditions or any conditions in terms of the invariant factors of A (X) are insufficient to guarantee the existence of solutions with a given set of invariant factors for XI -X is shown by the two equations We now pass to the description of an algorithm believed to be new for the solution of (8).…”

Section: If X Is a Solution Ofeaix^o Then The Determinant Of The Matmentioning

confidence: 99%

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Rational methods in matrix equations

Ingraham¹

1941

Bull. Amer. Math. Soc.

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“…Theorem 5, which is a corollary of a theorem due to Phillips,8 yields us an algorithm better than the W.P.A. This theorem is as follows : THEOREM …”

Section: Is a Solution Ofeaix { = 0 If And Only If\i-xisa Right Facmentioning

confidence: 95%

Section: If X Is a Solution Ofeaix^o Then The Determinant Of The Matmentioning

confidence: 99%

Rational methods in matrix equations

Ingraham¹

1941

Bull. Amer. Math. Soc.

Self Cite

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“…a standard system of linear equations that solves (11). The extension of this procedure to systems of equations of the form (11) is obvious.…”

Section: Tensor Equationsmentioning

confidence: 99%

Stretching and condensing tensors. Application to tensor and matrix equations

Tolosa¹,

Ron²

2006

ijcms

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Since tensors are vectors, no matter their order and valencies, they can be represented in matrix form and in particular as column matrices of components with respect to their corresponding bases. This consideration allows using all the available tools for vectors and can be extremely advantageous to deal with some interesting problems in linear algebra, as solving tensor linear equations. Once, the tensors have been operated as vectors, they can be returned to their initial notation as tensors. This technique, that is specially useful for implementing computer programs, is illustrated by several examples of applications. In particular, some interesting tensor and matrix equations are solved. Several numerical examples are used to illustrate the proposed methodology.

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