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"This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided."

"Misalkan U dan V adalah ruang vektor atas lapangan F. Hasil kali tensor (tensor product) dari U dan V adalah pasangan ruang vektor U_0 atas lapangan F dan pemetaan bilinier t:U×V→U_0, sedemikian sehingga (U_0,t) membentuk pasangan universal untuk bilinieritas (universal pair for bilinearity). Ruang vektor U_0 dinotasikan U⊗V. Yokonuma (1992) memberikan cara mengkonstruksi hasil kali tensor dari U dan V dengan menggunakan basis untuk U, V dan U_0. Roman (2008) memberikan cara lain untuk mengkonstruksi hasil kali tensor dari U dan V yaitu dengan menggunakan ruang hasil bagi F_(U×V)⁄S dan pemetaan bilinier t:U×V→F_(U×V)⁄S. Beberapa sifat yang dimiliki hasil kali tensor antara lain mengawetkan basis U dan V, anggota ruang vektor U_0 bersifat bilinier dan memiliki representasi tunggal, serta dapat membentuk isomorfisma antara himpunan pemetaan bilinier pada U×V dan himpunan transformasi linier pada U⊗V. Tugas akhir ini meninjau cara mengkonstruksi hasil kali tensor berdasarkan Yokonuma dan Roman, membahas beberapa sifatnya, dan memberikan contoh konstruksi hasil kali tensor dari R^2 dengan R^3 serta hasil kali tensor dari R^2 dengan M(2,2;R).

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Let U and V are vector spaces over a field F. Tensor product of U and V is a pair of a vector space U_0 over a field F and a bilinear map t:U×V→U_0 such that (U_0,t) is a universal pair for bilinearity. The vector space U_0 is denoted by U⊗V. Yokonuma (1992) gave a way to construct a tensor product of U and V with bases of U, V and U_0. Roman (2008) gave a different way to construct a tensor product of U and V. It is constructed by using a quotient space F_(U×V)⁄S and a bilinear map t:U×V→F_(U×V)⁄S. Some properties of the tensor product are that it preserves the base of U and V, the elements of the vector space U_0 have a bilinear property and a unique representation. Furthermore, the tensor product can form an isomorphism between a set of bilinear map on U×V and a set of linear transformation on U⊗V. This skripsi gives two constructions of the tensor product based on Yokonuma and Roman, discusses some of its properties and gives examples of tensor product of R^2and R^3and tensor product of R^2 and M(2,2;R)"