Basic Examples (4) 

Calculate the κ of a matrix w.r.t. 2-norm:

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For a 3⨯3 matrix:

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Condition number computed with machine precision:

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Symbolic calculation:

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Condition number of a complex matrix:

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Scope (5) 

Calculate the condition number corresponding to other norms:

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For any matrix A, κ(λ A)=κ(A)

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or for any complex constant as well:

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For a diagonal matrix D=diag(d_i), :

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Efficient of large computations depend on the efficiency of very efficient Norm:

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Condition number of sparse matrices:

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Condition number of structured matrices:

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IdentityMatrix[n] always has condition number 1:

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Condition number of HilbertMatrix grows exponentially:

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Properties and Relations (1) 

MatrixConditionNumber requires the first argument to be a square matrix:

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