In spite of the negative theoretical results on the joint spectral radius computability, methods have been proposed that perform well in practice.
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For instance, together with the spectral radius formula, it implies that the C *-norm is uniquely determined by the algebraic structure:
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Moreover, the spectrum \ sigma ( x ) of an element " x " is non-empty and satisfies the spectral radius formula:
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.. . a sufficient condition for convergence is that the spectral radius of the derivative is strictly bounded by one in a neighborhood of the fixed point.
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Perron numbers are named after Oskar Perron; the Perron Frobenius theorem asserts that, for a graph is defined to be the spectral radius of its adjacency matrix.
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The advantage of these methods is that they are easy to implement, and in practice, they provide in general the best bounds on the joint spectral radius.
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A bounded operator ( on a complex Hilbert space ) is called a "'spectraloid operator "'if its spectral radius coincides with its numerical radius.
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An advantage of these methods is that in the favorable cases it can find the exact value of the joint spectral radius and provide a certificate that this is the exact value.
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:If you type " spectral radius " into Wikipedia's search bar then you will find the talk ) 17 : 24, 15 February 2012 ( UTC)
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However, a general non-negative irreducible matrix " A " may possess several eigenvalues whose absolute value is equal to the spectral radius of " A ", so the statements need to be correspondingly modified.
