Advanced Modern Algebra

By J. Rotman. 2002

467 citations recorded by the source corpus.

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The classification of Leonard triples of QRacah type (2011, methodology): “Similarly we evaluate (3, 1)-entry of either side of (67) and obtain”
An Introduction to Clifford Algebras and Spinors (2016, unknown): “If Wi ∩Wj = {0} for i 6= j, and V = W1 +W2 + · · ·+Wn (i.e. for each v ∈ V , there are wi ∈ Wi with v = v1 + · · · + vn) (Rotman, 2000), then V is said to be the direct sum of the Wi subspaces, denoted by V = W1 ⊕W2 ⊕ · · · ⊕Wn = n⊕ i=1 Wi.”
Computational Algebraic Geometry (2003, background): “Supplemental Reading: some options for additional algebra background are Hungerford [56], Lang [59] or Rotman [81].”
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem (2006, unknown): “Even though tensors are well-studied objects in the standard graduate mathematics curriculum [1, 27, 41, 52, 63] and more specifically in multilinear algebra [9, 34, 59, 61, 78], a ‘tensor’ continues to be viewed as a mysterious object by outsiders.”