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Jon Peter May (born September 16, 1939, in New York) is an American mathematician working in the fields of algebraic topology, category theory, homotopy theory, and the foundational aspects of spectra. He is known, in particular, for the May spectral sequence and for coining the term operad.
Prior to Typhoon Yagi forming and making landfall in Vietnam, domestic media reported unusual weather patterns in August 2024. Speaking to the Natural Resources and Environment newspaper, Mai Văn Khiêm, Director of the National Center for Hydro-Meteorological Forecasting, stated that the country's average temperature reached 28.3 °C (82.9 °F), the highest in recorded history. [1]
As such, the proof may be written in the notation of tensor products. Then one may consider the multilinear map V × V ∗ × V × V ∗ → V ⊗ V ∗ given by sending (v, φ, w, ψ) to φ(w)v ⊗ ψ. Further composition with the trace map then results in φ(w)ψ(v), and this is unchanged if one were to have started with (w, ψ, v, φ) instead.
Multiplying a matrix M by either or on either the left or the right will permute either the rows or columns of M by either π or π −1.The details are a bit tricky. To begin with, when we permute the entries of a vector (, …,) by some permutation π, we move the entry of the input vector into the () slot of the output vector.
The polynomial p A in an indeterminate X given by evaluation of the determinant det(X I n − A) is called the characteristic polynomial of A. It is a monic polynomial of degree n. Therefore the polynomial equation p A (λ) = 0 has at most n different solutions, that is, eigenvalues of the matrix. [42] They may be complex even if the entries of ...
The positive operator P is the unique positive square root of the positive operator A ∗ A, and U is defined by U = AP −1. If A is not invertible, then it still has a polar composition in which P is defined in the same way (and is unique). The unitary operator U is not unique.
Mathematical Applications Group, Inc. (a.k.a. MAGi or MAGi/SynthaVision) was an early computer technology company founded in 1966 by Dr. Philip Mittelman and located in Elmsford, New York, where it was evaluating nuclear radiation exposure.
A polynomial matrix over a field with determinant equal to a non-zero element of that field is called unimodular, and has an inverse that is also a polynomial matrix. Note that the only scalar unimodular polynomials are polynomials of degree 0 – nonzero constants, because an inverse of an arbitrary polynomial of higher degree is a rational function.