A question about how find the canonical forms over R and C.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Real and complex canonical forms

Can you offer guidance or do you also need help?

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