Re: [eigen] on fuzzy comparisons |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] on fuzzy comparisons*From*: Benoît Jacob <jacob@xxxxxxxxxxxxxxx>*Date*: Thu, 5 Jun 2008 18:12:41 +0200*Cc*: "Gael Guennebaud" <gael.guennebaud@xxxxxxxxx>

> ***************************************************************** > m1 << m2 if and only if we have m1*v << m2*v for all vectors v > ***************************************************************** > > Sounds reasonable doesn't it? I am very attached to the fact that this > relation has such a simple geometrical meaning. The implemented algorithm > amounts to check that for v running over the canonical basis, and this is > equivalent to checking it for all vectors v. sorry, i must correct that. The current solution checks that m1 << m2 if and only if we have m1*v << m2*v for all vectors v for v = e_1, ...., e_n, the n vectors of the canonical basis. This is in fact not equivalent to checking that for all vectors v, although one direction obvously is true -- if it's true for all vectors v, then in particular it's true for v = e_1, ... , e_n. Now that we have matrixNorm() I am quite open to the idea of implementing matrix comparisons on top of it. At least that's mathematically satisfying. What's your opinion? Cheers, Benoit

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**References**:**[eigen] on fuzzy comparisons***From:*Gael Guennebaud

**Re: [eigen] on fuzzy comparisons***From:*Benoît Jacob

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