I want a solution to the whole matrix, not just the diagonal, in detail until I...
(3) Take the case of 3 states ji> i-1,2, 3 which are eigenfunctions of H with degenerate eigenenergies, represented in matrix form. 10 0 0 H(0) 10 10 01,Ιψο > 12 A perturbation Hamiltonian is applied to the original system H 0 0 10 of matrix 3 0 0] a-1 Fl("-Volo a , with the off-diagonal elements given by a and numerically 1 (a) Calculate the energies of the three states to first-order perturbation theory represented by H'- HHby adding...
Question B 7. (a) Let -1 0 0 (i) Find a unitary matrix U such that M-UDU where D is a diagonal matrix. 10 marks] (i) Compute the Frobenius norm of M, i.e., where (A, B) = trace(B·A). [4 marks] 3 marks] (iii) What is NM-illp? (b) Let H be an n × n complex matrix (6) What does it mean to say that H is positive semidefinite. (il) Show that H is positive semidefinite and Hermitian if and only...
Diagonal Difference HackerRank Pseudocode and C++: Given a square matrix, calculate the absolute difference between the sums of its diagonals. Function Description Complete the diagonalDifference function described below to calculate the absolute difference between diagonal sums. diagonalDifference( integer: a_size_rows, integer: a_size_cols, integer array: arr) Parameters: a_size_rows: number of rows in array a_size_cols: number of columns in array a: array of integers to process Returns: integer value that was calculated Constraints -100 < = elements of the matrix < = 100...
Please show all work in READ-ABLE way. Thank you so much in advance. Problem 2.2 n and let X ε Rnxp be a full-rank matrix, and Assume p Note that H is a square n × n matrix. This problem is devoted to understanding the properties H Any matrix that satisfies conditions in (a) is an orthogonal projection matriz. In this problem, we will verify this directly for the H given in (1). Let V - Im(X). (b) Show that...
I need help with Q12) please and eigenvectors of the row-echelon matrix VWV) 37dldl IV 31076 IW NO LOHS 1 U = 2 -4 0 2 1 0 0 3 0 0 0 3 --3 3 5 d the eigenvalues and eigenvectors of the following matrices. a) A= 1 3 0 2 2 0 0 0 6 3 0 b) B= 0 -4 0 6 0 -1 3 Problems 8.2 : Eigenvectors, bases, and diagonalisation 11. [R] For each of...
Let M be an n x n matrix with each entry equal to either 0 or 1. Let mij denote the entry in row i and column j. A diagonal entry is one of the form mii for some i. Swapping rows i and j of the matrix M denotes the following action: we swap the values mik and mjk for k = 1,2, ... , n. Swapping two columns is defined analogously. We say that M is rearrangeable if...
Sur I Nano 2019/20) Qunntum physics exercices 1.1 Linear algebra and formalism Exercice 1.1.1 Basic calculations We consideran llibert prace Ey of dimension 2 and the two following vectors of En = (17.) and le >= () acting on vectors of Eh 21- We consider also the linear operator = 1+5 1 Calculate the square norms of the two vectors < Hermitian scalar products <ul> and < > 2. Calculate the eigensalues and cigarvectors of A. >, < > and...
Q4: Solve the payoff matrix Example-1 Player B П I III IV V -2 0 0 5 Player A III II 3 2 2 7 4 0 -2 6 IV 5 3 4 2 -6 Q5: Determine the maximum and minimum values of the function: f(x)= 12x-45x 40x' +5 Q6: Find the second order Taylor's series approximation of the function ) =x}x, +xe about the point х*- Q7: Find the extreme points of the function f(x,x)xx+2x + 4x +6 Q8:...
Given a matrix, clockwise-rotate elements in it. Please add code to problem3.cpp and the makefile. I have also given the main_problem3.cpp and problem3.h to test. problem3.cpp::: #include "problem3.h" // A function to rotate a matrix mat[][MAX] void rotatematrix(int m, int n, int mat[][MAX]) { // your code here } Makefile::: all : problem3.o g++ -o mainp3 # your code here problem3.o : problem3.h problem3.cpp # your code here clean: rm -f *.o mainp3 main_problem3.cpp::: #include <iostream>...
Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...