GEOMETRY, TOPOLOGY AND PHYSICS

... working in particle physics, condensed matter physics and general relativity. The lectures were quite informal and I have tried to keep this informality as much as possible in this book. The proof of a theorem is given only when it is instructive and not very technical; otherwise examples will make ...

... working in particle physics, condensed matter physics and general relativity. The lectures were quite informal and I have tried to keep this informality as much as possible in this book. The proof of a theorem is given only when it is instructive and not very technical; otherwise examples will make ...

Sheldon Axler Third Edition

... deﬁned in this chapter as the sum of the eigenvalues and the product of the eigenvalues, both counting multiplicity. These easy-to-remember deﬁnitions would not be possible with the traditional approach to eigenvalues, because the traditional method uses determinants to prove that sufﬁcient eigenval ...

... deﬁned in this chapter as the sum of the eigenvalues and the product of the eigenvalues, both counting multiplicity. These easy-to-remember deﬁnitions would not be possible with the traditional approach to eigenvalues, because the traditional method uses determinants to prove that sufﬁcient eigenval ...

Linear Algebra

... is that the third chapter on linear maps does not begin with the definition of homomorphism. Instead it begins with the definition of isomorphism, which is natural: students themselves observe that some spaces are “the same” as others. After that, the next section takes the reasonable step of isolat ...

... is that the third chapter on linear maps does not begin with the definition of homomorphism. Instead it begins with the definition of isomorphism, which is natural: students themselves observe that some spaces are “the same” as others. After that, the next section takes the reasonable step of isolat ...

The geometry of orthogonal groups over finite fields

... The assertion of Proposition 2.1 is also a consequence of the Witt’s extension theorem (see Theorem A.6). Indeed, the Witt’s extension theorem implies that the group of isometries acts transitively on the set of maximal singular subspaces. Yet another proof of this fact will be given in Appendix B. ...

... The assertion of Proposition 2.1 is also a consequence of the Witt’s extension theorem (see Theorem A.6). Indeed, the Witt’s extension theorem implies that the group of isometries acts transitively on the set of maximal singular subspaces. Yet another proof of this fact will be given in Appendix B. ...