| 1. | Not all matrices have an inverse ( see invertible matrix ).
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| 2. | Notice that the polar decomposition of an invertible matrix is unique.
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| 3. | The case of a square invertible matrix also holds interest.
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| 4. | See also Invertible matrix .-IMSoP 13 : 39, 19 Apr 2004 ( UTC)
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| 5. | More generally, if is any invertible matrix, and is an eigenvalue of with generalized eigenvector, then.
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| 6. | In addition to providing a computational tool, this formula demonstrates that a matrix exponential is always an invertible matrix.
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| 7. | That is, there exists an invertible matrix M such that J = M ^ {-1 } AM.
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| 8. | For some invertible matrix, the matrix of components of the metric changes by " A " as well.
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| 9. | The corresponding article ( Invertible matrix # Applications ) has some uses of it, but often inverting can be avoided.
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| 10. | One can write down the inverse of an invertible matrix by computing its cofactors by using Cramer's rule, as follows.
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