Complex n-tuples, Basis and Diagonalization

Related BrainMass Solutions

• theory regarding diagonalization

  So, if there are n distinct eigenvalues, there is a set of n linearly independent eigenvectors and this forms a basis of V.

• Transformations : Diagonalization of Matrices

  Diagonalization of a matrix is investigated. The solution is well presented.

• Linear Algebra : Diagonalizing Matrices

  For each k between 0 and n, consider the case when the nullity of B is k.)

• Operations for Polynomials and Vector Space

  . + a_(n-1)x^(n-1) where a_i belongs to F. Let F be a field and let V be the totality of all ordered n-tuples, (a_0, a_1, a_2, ... a_n) where the a_i belongs to F.

• Proof : Diagonalization of Matrices

  Given the following theorem and definition: Let A be a square matrix of order n. Assume that A has n distinct eigenvalues. Then A is diagonalizable. And A matrix is diagonalizable if it is similar to a diagonal matrix.

• Initial Value Problem, Ordinary Differential Equation: Jordan and Diagonalization

  Initial value problems and ordinary differential equations are solved by using Jordan and Diagonalization.

• Real Analysis : In this space, is every closed and bounded set compact?

  It says, a subset S of Eucliean space R^n is bounded and closed if and only if S is compact. From the condition, every subset of X is also a subset of R^n. Sometimes in R^n, the compactness is defined by bounded and closed set.

• # problems in Quantum Mechanics

  [x,p^n] = ihn*p^(n-1) c. show that if f(x) can be expanded in polynomial in x and g(p) can be expanded in a polynomial in p, then [f(x),p] = ih*df/dx and [x,g(p)] = ih * dg/dp for problem 3 that deals with Hamiltonian, observables, diagonalization

• Radical Ideals

  Here A^n is affine n-space over a fixed algebraically closed field i.e. is the set of all n-tuples of elements of that algebraically closed field question asks to show that "ideal of an algebraic variety is radical" Please see the attached file for the