Norms and the spectral radius of matrices
نویسندگان
چکیده
منابع مشابه
The generalized spectral radius and extremal norms
The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generali...
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We generalize in various directions a result of Friedland and Karlin on a lower bound for the spectral radius of a matrix that is positively diagonally equivalent to a • The research of these authors was supported by their joint grant No. 90-00434 from the United States-Israel Binational Science Foundation, Jerusalem, Israel. t The research of this author was supported in part by NSF Grant DMS-...
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In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...
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We give lower bounds for the spectral radius of nonnegative matrices and nonnegative symmetric matrices, and prove necessary and sufficient conditions to achieve these bounds.
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If ρ(A) > 1, then lim n→∞ ‖A‖ =∞. Proof. Recall that A = CJC−1 for a matrix J in Jordan normal form and regular C, and that A = CJnC−1. If ρ(A) = ρ(J) < 1, then J converges to the 0 matrix, and thus A converges to the zero matrix as well. If ρ(A) > 1, then J has a diagonal entry (J)ii = λ n for an eigenvalue λ such that |λ| > 1, and if v is the i-th column of C and v′ the i-th row of C−1, then ...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1962
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1962.100539