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For MIMO systems, this quantity is the peak gain over all frequencies and all input directions, which corresponds to the peak value of the largest singular value of sys. So I didn't test for the for loop and Divkar's bsxfun, but you can see that for arrays smaller than 3e4 kron is better than bsxfun, and this changes at larger arrays (ratio of <1 means kron took less time given the size of the array). n norm(sys,Inf) returns the L norm (Control System Toolbox) of sys, which is the peak gain of the frequency response of sys across frequencies. Matlab provides three functions for computing condition numbers: cond, condest, and nd computes the condition number according to Equation (), and can use the one norm, the two norm, the infinity norm or the Frobenius norm. And here it is: range=3*round(logspace(1,6,200)) If the inverse does not exist, then we say that the condition number is infinite. So I tried to check using timeit my two solutions (because they are one liners it's easy).
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Ok, this got me curios, as I know bsxfun starts to be less efficient for bigger array sizes. Here's a bsxfun solution (less elegant, but hopefully faster): 3 1])),3,)' Note that norm(A), where A is an n-element vector, is the length of A.A slightly shorter and vectorized way will be (if a is your matrix) : b=a-kron(a(1:3:end,:),ones(3,1)) norm(A30) will return A302, or more generally. Though your activity may be recorded, a page refresh may be needed to fill the banner 0/1. The norm of a matrix and the norm of a vector are different things, and they have different definitions. To obtain the root-mean-square (RMS) value, use norm(A)/sqrt(n). 1: MATLAB: Norms and Distances This tool is provided by a third party. Returns sum(abs(A).^ p )^(1/ p ), for any 1 p. When A is a vector, slightly different rules apply: The Frobenius-norm of matrix A, sqrt(sum(diag(A'* A))). T he infinity norm, or largest row sum of A, max(sum(abs(A'))). If this integral is finite, then the signal e is square integrable, denoted as e. We will often use the 2-norm, ( L2 -norm), for mathematical convenience, which is defined as. The largest singular value (s ame as norm(A)). There are several ways of defining norms of a scalar signal e ( t) in the time domain. The 1-norm, or largest column sum of A, max(sum(abs((A))). Returns a different kind of norm, depending on the value of p: Returns t he largest singular value of A, max(svd(A)). If sys is a model that has tunable or uncertain parameters, then hinfnorm evaluates the H. If sys is an unstable system, then the H norm is defined as Inf. If sys is a stable MIMO system, then the H norm is the largest singular value across frequencies. The norm function calculates several different types of matrix norms: If sys is a stable SISO system, then the H norm is the peak gain, the largest value of the frequency response magnitude. The norm of a matrix is a scalar that gives some measure of the magnitude of the elements of the matrix. Norm (MATLAB Function Reference) MATLAB Function Reference This video discusses how least-squares regression is fragile to outliers, and how we can add robustness with the L1 norm.