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mattbaker.blog | ||
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alanrendall.wordpress.com
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| | | | | The theorem of the title is about dividing smooth functions by other smooth functions or, in other words, representing a given smooth function in terms of products of other smooth functions. A large part of the account which follows is based on that in the book 'Normal Forms and Unfoldings for Local Dynamical Systems' by... | |
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www.jeremykun.com
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| | | | | Last time we defined and gave some examples of rings. Recapping, a ring is a special kind of group with an additional multiplication operation that "plays nicely" with addition. The important thing to remember is that a ring is intended to remind us arithmetic with integers (though not too much: multiplication in a ring need not be commutative). We proved some basic properties, like zero being unique and negation being well-behaved. | |
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nhigham.com
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| | | | | The Cayley-Hamilton Theorem says that a square matrix $LATEX A$ satisfies its characteristic equation, that is $latex p(A) = 0$ where $latex p(t) = \det(tI-A)$ is the characteristic polynomial. This statement is not simply the substitution ``$latex p(A) = \det(A - A) = 0$'', which is not valid since $latex t$ must remain a scalar... | |
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halfaphotograph.wordpress.com
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| | | How unappealing these delectable bites of food would look if not for the zigzagged dash of sauce! | ||
