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Real and complex canonical forms

  1. Dec 3, 2008 #1
    A question about how find the canonical forms over R and C.
    An example, given a quadratic form,q(x,y,z)=x^2 + 2xy + 4yz + z^2
    find the canonical forms over R and C.

    First step,i get the matrix 1 2^0.5 0
    2^0.5 0 2
    0 2 1
    then by doing the double operation
    i get the identiy matrix.
    the canonical form over R is diag(I_r, -I_s, O_t)
    and the canonical form over C is diag(I_r,0_t)
    is the canonical form unique?
    what are the final anwsers?

    I know that any matrix can be changed to Identity matrix or a matrix with a 0 row.
    does it mean most matries have similar canonical form?
  2. jcsd
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