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homotopytypetheory.org | ||
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sitr.us
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| | | | | Dependent types provide an unprecedented level of type safety. A quick example is a type-safe printf implementation. They are also useful for theorem proving. According to the Curry-Howard correspondence, mathematical propositions can be represented in a program as types. An implementation that satisfies a given type serves as a proof of the corresponding proposition. In other words, inhabited types represent true propositions. | |
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kuruczgy.com
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bentnib.org
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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... | ||
