Show that an arbitrary square matrix with elements wij can b
Question and Solution
Show that an arbitrary square matrix with elements wij can be written in the form wij = wS ij + wA ij where wS ij and wA
88 % (998 Review)
Show that an arbitrary square matrix with elements wij can be written in the form wij = wS ij + wA ij where wS ij and wA ij are symmetric and anti-symmetric matrices, respectively, satisfying wS ij = wS ji and wA ij = ?wA ji for all i and j. Now consider the second order term in a higher order polynomial in D dimensions, given by D i=1 D j=1 wijxixj . (1.131) Show that D i=1 D j=1 wijxixj = D i=1 D j=1 wS ijxixj (1.132) so that the contribution from the anti-symmetric matrix vanishes. We therefore see that, without loss of generality, the matrix of coefficients wij can be chosen to be symmetric, and so not all of the D2 elements of this matrix can be chosen independently. Show that the number of independent parameters in the matrix wS ij is given by D(D + 1)/2.
Your answer will be ready within 2-4 hrs. Meanwhile, check out other millions of Q&As and Solutions Manual we have in our catalog.
Crazy for Study is a platform for the provision of academic help. It functions with the help of a team of ingenious subject matter experts and academic writers who provide textbook solutions to all your course-specific textbook problems, provide help with your assignments and solve all your academic queries in the minimum possible time.
Copyright@2020 Crazy Prep Pvt. Ltd. (Crazy For Study)
Disclaimer: Crazy For Study provides academic assistance to students so that they can complete their college assignments and projects on time. We strictly do not deliver the reference papers. This is just to make you understand and used for the analysis and reference purposes only.