Matrix norm

Related BrainMass Solutions

• Matrix Norm, Condition Number and Singular and Non-Singular Matrix

  Matrix Norm, Condition Number and Singular and Non-Singular Matrix are investigated. The solution is detailed and well presented.

• Numerical analysis proof

  Thanks Recall that a given vector norm |X| the operator norm of matrix A is given by ...... Hello Please find the solution in the attached file.

• Norm on Linear system with matrix A

  503825 Norm on Linear System with Matrix A We fix a norm II . II on R^n. If A is a real n x n matrix, define The norm II A II = sup { II Ax II : x E R^n, II x II =< 1}.

• Proof in Linear Algebra

  Similarly, the subordinate matrix norm ||A||_infinity is the maximum absolute row sum of A, i.e. ||A||_infinity = max(|a|+|b|,|b|+|a|) = |a|+|b|. The subordinate matrix norm ||A||_2 is given by ||A||_2 = max_{x!=0}(||Ax||_2/||x||_2).

• Matrix : Convergence, Pseudoinverse and Single Value Decomposition

  The spectral radius is the maximum size of these eigenvalues and it is denoted by: Theorem 1: Let A be an arbitrary square matrix of order n. then for every matrix norm we have: .

• Rayleigh Quotients and Error Bonds

  Or the error bound can be estimated using the formula: |  - xA|  || A*x - max * x|| / || x||   Where ||A||F = [Trace (ATA)]1/2, the Frobenious norm or norm of a square matrix.

• Numerical Methods Proofs

  b) consider the matrix 4 2 1 A = 2 5 -2 1 -2 7 Compute ||A||_infinity and find a vector x such that ||A||_infinity = ||A_x|| / ||x||_infinity.

• Ill-Conditioned Systems of Equations

  In part 1 in this question I have already found norm and the norm says it is ill-conditioned.

• Vectors and Matrices : Operations and Transformations

  Find a) ||u + v|| b) ||u|| + || v || c) Find two vectors in R³ with norm 1 orthogonal to be both u and v d) Find norm of vector u / || u || 2) For which values of t are vectors u = (6, 5, t), and v = (1,t,t) orthogonal?