1. T

    matrix inverse and diagonalisation proof

    since Q^{-1}BQ and Q^{-1}CQ are diagonal matrix, than Q^{-1}BQ = Q^{-1}CQ as Q diagonalises B and C. Q is invertible, so multiply both sides by Q QQ^{-1}BQ = QQ^{-1}CQ = BQ = CQ BQQ^{-1} = CQQ^{-1} B = C since they are equal BC = CB Is this correct?
  2. R

    Diagonalisation of Matrices..

    Ok So i am understanding that any M matrix can be rewritten such that M= UDU^-1, where U consists of the matrix consisting of the eigenvectors and D is the diagonal matrix consisting of eigenvalues. Is there another way to think about this idea through transformations? i.e 1. How does the...
  3. V

    non diagonalisable matrix

    Hello everyone!Can anyone help me please ? I've got a serious problem in maths with the non-diagonalisable matrices! A is a matrix [3 1 0] [-4 -1 0] [4 -8 -2] det |A-λI| = (-2-λ)(λ-1)^2 Thus, we find 2 eigen values: λ= -2 (order 1) λ= 1 (order...
  4. I

    Diagonalisation of symmetric matricies

    I have just learnt how to reduce a symmetric matrix to a diagonal one, using the equation below: D={P}^{T}AP Where A is the original symmetric matrix and D is the diagonal matrix. P is an orthogonal matrix whose columns consist of the normalised eigenvectors of A. My problem is how to write...
  5. P

    Real Analysis / Cantors Diagonalisation possibly? S is the set of f:N->{0,1,2}

    Hey all, i've come across a problem i'm stumped on: Let S be the set of all functions u: N -> {0,1,2} Describe a set of countable functions from S We're given that v1(n) = 1, if n = 1 and 2, if n =/= 1 The function above is piecewise, except i fail with latex To begin...
  6. V

    matrix diagonalisation - real and complex matrices - some observations

    I am revising Linear Algebra and trying to put together a rule how to decide whether a matrix is diagonaliseable. (a short and simple rule that can be referred to immediately when solving a problem) This is what I came up based on my experience with solving questions and comparing to model...
  7. N

    Diagonalisation of a matrix

    anyone help me on this. the eigenvectors are 2,-1,3. This is B, 1 1 1 2 1 2 3 2 4 This is B-1, 0 2 -1 2 -1 0 -1 -1 1 I cant seem to workout how you manage to get from B to B-1.