Recent content by han35

  1. H

    Expressing a symmetric matrix in terms on eigenvalues/vectors

    Does anyone know why? If A is a symmetric matrix then A can be expressed as: ## A = ## \displaystyle \sum_{j=1}^{n}λ_j(A)v_jv^T_j\ where ##v_j, j = 1, 2, . . . , n.## are the eigenvectors of ##A## But why?
  2. H

    Expressing a symmetric matrix in terms on eigenvalues/vectors

    Ok, so after testing some symmetric 3x3 matrices and computing it by hand I can confirm that the ##v_j##'s are indeed the eigenvectors of ##A##. Now I just need to know why, lol.
  3. H

    Expressing a symmetric matrix in terms on eigenvalues/vectors

    Homework Statement Generate a random 10 x 10 symmetric matrix A (already done in MATLAB) . Express A in the formHomework Equations ## A = ## \displaystyle \sum_{j=1}^{10}λ_j(A)v_jv^T_j\ for some real vectors ##v_j, j = 1, 2, . . . , 10.## The Attempt at a Solution I'm pretty sure the...