From Vectors to TensorsIt is true that there exist many books dedicated to linear algebra and some what fewer to multilinear algebra, written in several languages, and perhaps one can think that no more books are needed. However, it is also true that in algebra many new results are continuously appearing, different points of view can be used to see the mathematical objects and their associated structures, and different orientations can be selected to present the material, and all of them deserve publication. Under the leadership of Juan Ramon Ruiz-Tolosa, Professor of multilin ear algebra, and the collaboration of Enrique Castillo, Professor of applied mathematics, both teaching at an engineering school in Santander, a tensor textbook has been born, written from a practical point of view and free from the esoteric language typical of treatises written by algebraists, who are not interested in descending to numerical details. The balance between follow ing this line and keeping the rigor of classical theoretical treatises has been maintained throughout this book. The book assumes a certain knowledge of linear algebra, and is intended as a textbook for graduate and postgraduate students and also as a consultation book. It is addressed to mathematicians, physicists, engineers, and applied scientists with a practical orientation who are looking for powerful tensor tools to solve their problems. |
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Common terms and phrases
anti-symmetric tensor associated tensor axis basic vectors block change-of-basis changes of basis column contracted tensor product contravariant coordinates contravariant tensor corresponding cos² covariant coordinates covariant indices data tensor Determine dot product dual ē¹ ē₂ equation Euclidean space Euclidean tensor Example expression exterior algebra exterior product exterior tensor exterior vectors factor Formula fundamental metric tensor given tensor Gram matrix homogeneous tensor initial basis isometry Kronecker delta linear space linear subspace matrix form matrix representation mixed exterior mixed tensor modular tensor multilinear notation number of strict obtain orthogonal permutation Poooo respect rotation Solution strict components subspace symmetric tensor system of scalars tensor algebra tensor character tensor contraction tensor nature tensor of order tensor product tensor space Theorem V₁ Vn(K αβ αβγ оо оо ооо