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  1. L

    Prove if a Square Matrix A is Diangonalizable

    Okay, completely forgetting about the span, how else would you find the eigenvectors?
  2. L

    Prove if a Square Matrix A is Diangonalizable

    The span of the kernel is an eigenvector for the corresponding eigenvalue, is it not?
  3. L

    Prove if a Square Matrix A is Diangonalizable

    So, for eigenvalue=0, you just find the kernel of matrix A and the span will be one of the eigenvectors? What about for eigenvalue=10?
  4. L

    Prove if a Square Matrix A is Diangonalizable

    Since the rank is m, the matrix is not full rank. Therefore, is the other eigenvalue 0?
  5. L

    Prove if a Square Matrix A is Diangonalizable

    Okay so we know that an eigenbasis consists of eigenvectors. We know one of the eigenvalues, 10. But, how do you find the other eigenvalues and corresponding eigenvectors?
  6. L

    Prove if a Square Matrix A is Diangonalizable

    Homework Statement Let A be a non-diagonal n-by-n matrix of rank m. Suppose that a set of vectors, v1 ... vm, are linearly independent vectors in Rn such that for i = 1,...,m, Avi = 10vi (vi is a vector in the given set of linearly independent vectors). (a) Prove that A is diagonalizable...
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