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is a norm on the vector space Mn(K), with the additional property called submultiplicativity that kABk kAkkBk, for all A,B 2 Mn(K). A norm on matrices satisfying the above property is often called a submultiplicative matrix norm. Since I2 = I,fromkIk = I2 kIk2,wegetkIk1, for every matrix norm.

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View ORF523_S17_Lec2_gh.pdf from MATH 304 at Texas A&M University. ORF 523 Lecture 2 Instructor: A.A. Ahmadi Scribe: G. Hall Spring 2017, Princeton University Thursday, February 9, 2017 When in doubt
The submultiplicative property for matrix norms is defined and it is shown that the Frobenius norm is submultiplicative. The 2-norm is the most complicated norm to compute. Begin with the symmetric matrix A T A whose eigenvalues are nonnegative. A singular value. Description. For matrices. norm(x) or norm(x,2) is the largest singular value of x ...
Submultiplicative Matrix Norms If the norm also satisﬁes kABk≤kAkkBk, it is called submultiplicative. All induced matrix norms are submultiplicative. Frobenius-norm or Hilbert-Schmidt norm (submultiplicative, but not an induced norm) kAk F = X i,j |a ij|2 1/2 = Trace(ATA) 1/2 20/25
k·k will denote a vector norm on Cn and also a submultiplicative matrix norm on Cn,n which in addition is subordinate to the vector norm. Thus for any A,B ∈ Cn,n and any x ∈ Cn we have kABk ≤ kAkkBk and kAxk ≤ kAkkxk. This is satisﬁed if the matrix norm is the operator norm corresponding to the given vector norm or the Frobenius norm.
norms. In children with the decreased tissue iron stores, its absorption from the food is not increased, but decreased. It is associated with the reduction of enzyme activity of ferrum absorption in the child's...
The matrix 1-norm and 1-norm are given by kAk 1 = max j X i jA ijj kAk 1= max i X j jA ijj: These norms are nice because they are easy to compute. Also easy to compute (though it's not an induced operator norm) is the Frobenius norm kAk F = p tr(AA) = sX i;j jA ijj2: The Frobenius norm is not an operator norm, but it does satisfy the submul-
This norm is called the matrix norm subordinate to the vector norm. Prom the definition it follows It is an easy exercise to show that subordinate matrix norms are submultiplicative, i.e., whenever the...