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I've learned the process of orthogonal diagonalisation in an algebra course I'm taking...but I just realised I have no idea what the point of it is.

The definition is basically this: "A matrix A is orthogonally diagonalisable if there exists a matrix P which is orthogonal and D = PtAP where D is diagonal". I don't understand the significance of this though...what is special/important about this relationship?

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    For me, this is really one of those "always wanted to know but have always been afraid to ask" kind of questions. +12011-02-19
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    Consider the quadratic $x^{\rm t}Ax=1$ for $x\in\mathbb{R}^n$. Then, orthogonal diagonalization reduces this to a rotation of one the standard forms (ellipse or hyperbola if $n=2$).2011-02-19

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