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mattbaker.blog | ||
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qchu.wordpress.com
In this post we'll describe the representation theory of theadditive group scheme$latex \mathbb{G}_a$ over a field $latex k$. The answer turns out to depend dramatically on whether or not $latex k$ has characteristic zero. Preliminaries over an arbitrary ring (All rings and algebras are commutative unless otherwise stated.) The additive group scheme $latex \mathbb{G}_a$ over... |
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pfzhang.wordpress.com
Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... |
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nhigham.com
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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arkadiusz-jadczyk.eu
We continue Becoming anti de Sitter. Every matrix $\Xi$ in the Lie algebra o(2,2) generates one-parameter group $e^{\Xi t}$ of linear transformations of $\mathbf{R}^4.$ Vectors tangent to orbits of this group form a vector field. Let us find the formula for the vector field generated by $\Xi. |
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