Consider a quadratic form q on with symmetric matrix A, with rank A = r. Suppose that A has p positive eigenvalues, if eigenvalues are counted with their multiplicities. Show that there exists an orthogonal basis such that . Hint: Modify the approach outlined in and 65.
The diagonalizability of a quadratic form and definiteness property are used here to prove this.
It is proved using diagonalizability of a quadratic form and definiteness property.
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