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matrix condition number is greater or equal to 
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(Theorem)
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Proof. Let $ A$ be a square matrix. Then by properties of a matrix norm,
$$1=\vert\vert\,I\,\vert\vert =\vert\vert\,A A^{-1}\,\vert\vert \leq \vert\vert\,A^{-1}\,\vert\vert \vert\vert\,A\,\vert\vert.$$ 
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"matrix condition number is greater or equal to  " is owned by georgiosl.
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Cross-references: matrix norm, properties, square matrix, matrix condition number
This is version 7 of matrix condition number is greater or equal to  , born on 2005-08-16, modified 2006-10-14.
Object id is 7324, canonical name is PropertyOfMatrixConditionNumber.
Accessed 3387 times total.
Classification:
| AMS MSC: | 15A12 (Linear and multilinear algebra; matrix theory :: Conditioning of matrices) | | | 65F35 (Numerical analysis :: Numerical linear algebra :: Matrix norms, conditioning, scaling) |
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Pending Errata and Addenda
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