Results 281 to 290 of about 670,467 (323)
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Logarithmic Norms for Matrix Pencils
SIAM Journal on Matrix Analysis and Applications, 1999Summary: The author extends the usual concepts of least upper bound norm and logarithmic norm of a matrix to matrix pencils. Properties of these seminorms and logarithmic norms are derived. This logarithmic norm can be used to study the growth of the solutions to linear variable coefficient differential-algebraic systems.
Higueras, Inmaculada +1 more
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Siberian Mathematical Journal, 1967
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Linear and Multilinear Algebra, 2002
We consider approximation numbers for some norms on matrices, and look at the question when a closest rank h p approximant can be chosen to reduce the rank of a matrix by p . If the latter is always possible, we call the norm rank p reducing. It is easily seen that any unitarily invariant norm is rank p reducing.
K. Okubo, H.J. Woerdeman
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We consider approximation numbers for some norms on matrices, and look at the question when a closest rank h p approximant can be chosen to reduce the rank of a matrix by p . If the latter is always possible, we call the norm rank p reducing. It is easily seen that any unitarily invariant norm is rank p reducing.
K. Okubo, H.J. Woerdeman
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Vector Norm. Matrix Norm. Matrix Measure
1991Norms are widespread in the techniques of uncertain modelling and robust control. Multivariable systems and the state-space representation require valuating vectors and matrices by a single number. Most of the important relations for norms are listed or derived in this chapter. This material may be considered as a kind of reference, and the chapter may
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2017
In this chapter the concept of a norm on the vector space \({\mathbb {C}}^n\) is introduced. We investigate relationships between different norms. We give the definition of a norm on the space of complex rectangular matrices and study its properties in detail, particularly with regard to estimates of eigenvalues and singular values of operators.
Larisa Beilina +2 more
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In this chapter the concept of a norm on the vector space \({\mathbb {C}}^n\) is introduced. We investigate relationships between different norms. We give the definition of a norm on the space of complex rectangular matrices and study its properties in detail, particularly with regard to estimates of eigenvalues and singular values of operators.
Larisa Beilina +2 more
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2010
In multidimensional calculus, vector and matrix norms quantify notions of topology and convergence [2, 4, 5, 6, 8, 12]. Because norms are also devices for deriving explicit bounds, theoretical developments in numerical analysis rely heavily on norms.
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In multidimensional calculus, vector and matrix norms quantify notions of topology and convergence [2, 4, 5, 6, 8, 12]. Because norms are also devices for deriving explicit bounds, theoretical developments in numerical analysis rely heavily on norms.
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Quick Stability Checks and Matrix Norms
Economica, 1973Consider the difference equation system yt=b+Ayt-i; where yt is an nXl variable vector, b is an nXl constant vector and A is an nXn constant matrix. The fundamental necessary and sufficient stability condition for the system is /x(^)< 1, where [J.(A) is the modulus of the characteristic root of A of largest modulus.
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1975
In the last chapter we stressed one property of a set of vectors — that of linear independence. We now look at another property possessed by both vectors and matrices, that of ‘size’ or ‘magnitude’. We often want to be able to say that one vector is, in some sense, ‘bigger’ than another.
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In the last chapter we stressed one property of a set of vectors — that of linear independence. We now look at another property possessed by both vectors and matrices, that of ‘size’ or ‘magnitude’. We often want to be able to say that one vector is, in some sense, ‘bigger’ than another.
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Bounded-Norm Matrix-Inverse Mappings
IMA Journal of Numerical Analysis, 1990This paper introduces the concept of bounded-norm matrix-inverse mappings, i.e. mappings μ: R m×n →R nxm such that, for all nonzero m×n matrices A, the matrix μ(A) is a generalized inverse of A and ||μ(A)|| 0 is a constant and s(A) in the nonzero singular value of A having smallest absolute value.
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Matching with matrix norm minimization
1994Given (r1,r2,...r n ) ∈ R n , for any I=(I1,I2,...I n ) ∈ Z n , let E I =(e ij ), where e ij =(r i −r j )−(I i −I i ), find I ∈ Z n such that ∥E I ∥ is minimized, where ∥·∥ is a matrix norm. This is a matching problem where, given a real-valued pattern, the goal is to find the best discrete pattern that matches the real-valued pattern. The criterion of
Shouwen Tang, Kaizhong Zhang, Xiaolin Wu
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