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g-w1.github.io | ||
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richardzach.org
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| | | | | Paolo Mancosu, Sergio Galvan, and Richard Zach. An Introduction to Proof Theory: Normalization, Cut-elimination, and Consistency Proofs. Oxford: Oxford University Press, 2021. DOI: 10.1093/oso/9780... | |
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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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mikespivey.wordpress.com
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| | | | | It's fairly well-known, to those who know it, that $latex \displaystyle \left(\sum_{k=1}^n k \right)^2 = \frac{n^2(n+1)^2}{4} = \sum_{k=1}^n k^3 $. In other words, the square of the sum of the first n positive integers equals the sum of the cubes of the first n positive integers. It's probably less well-known that a similar relationship holds... | |
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chava61photography.photo.blog
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