Linear Algebra

By Jim Hefferon. 2012

2,313 citations recorded by the source corpus.

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Citations in the corpus

Data Encoding for Byzantine-Resilient Distributed Optimization (2019, methodology): “Note that we can always ﬁnd the basis vectors of N ( F ) by reducing F to its row-reduced-echelon-form (RREF) using the Gaussian elimination [HK71].”
Anti-Retroactive Interference for Lifelong Learning (2022, background): “, 1] and an eigenvalue λ = 1 associated with μ [1], i.”
Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability (2013, background): “do not change the determinants of the matrices H1 to HJ [37, 38], so that, finally, the determinant of the triangular matrix HJ is of form det(zI − Ã) = det [ Iz(zI −A + S1) ]”
Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A (2015, background): “For a textbook presentation of linear algebra, see Lang [345], and for the basics of groups and rings, see Dummit– Foote [151].”
The Theory of Quantum Information (2018, background): “Several textbooks cover the material on linear algebra summarized in this chapter; the classic books of Halmos [89] and Hoffman and Kunze [103] are two examples.”
Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging (2010, background): “The matrix is a Vandermonde matrix and therefore has full column rank [11], [16] as long as and the time-delays are distinct, i.”
Mathematics for Machine Learning (2020, methodology): “This chapter is mostly based on the lecture notes and books by Drumm and Weil (2001), Strang (2003), Hogben (2013), Liesen and Mehrmann (2015), as well as Pavel Grinfeld’s Linear Algebra series.”
Determinants and the volumes of parallelotopes and zonotopes (2010, background): “Why are determinants and parallelotopes so intimately connected in the first place? One answer is that the oriented volume of an n-parallelotope in n-space and the determinant are each the unique alternating, multilinear function of the generating vectors taking the value 1 on the identity matrix or”
Commuting Graphs of Matrix Algebras (2008, methodology): “By the primary decomposition theorem (Hoffman and Kunze, 1971, p. 220) and with no loss of generality, we may write A = A1 ⊕ · · · ⊕ Ak, where the minimal polynomials of matrices A1 Ak are irreducible and distinct.”