Introduction to Linear Algebra, 5th Edition
$\begingroup$ Well, then yes: a traceless matrix is similar (even unitarily) to a matrix with all its diagonal entries equal to zeroat least in characteristic zero. In positive characteristic I'm not quite sure, though the unitary thing goes down, of course. $\endgroup$ – DonAntonio Sep 21 '13 at 16:56 Trace (linear algebra) - formulasearchengine The special linear group consists of the matrices which do not change volume, while the special linear algebra is the matrices which infinitesimally do not change volume. In fact, there is an internal direct sum decomposition g l n = s l n ⊕ k {\displaystyle {\mathit {gl}}_{n}={\mathit {sl}}_{n}\oplus k} of operators/matrices into traceless On isometry groups of self-adjoint traceless and skew Mar 15, 2018
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The general linear algebra gl(V) is the algebra su(2), described as the algebra of 2 × 2 traceless antihermitian matrices. Although the matrices have complex entries, the vector space is naturally real – complex multiplication ruins antihermiticity.
Linear Transformations
LINEAR ALGEBRA HOMEWORK 1 SOLUTIONS JAMES CUMMINGS Total points: A1=10, A2 = 10, A3 = 10, B1 = 5, B2 = 10, c1 = 5, c2 = 5, C3 =20 for a total of 75 any traceless matrix is a sum of matrices of the form AB BA.It its actually true that any traceless matrix is of form AB BAbut the proof