Joshi A. Matrices and Tensors in Physics 2ed 1975

Textbook in PDF format

This updated edition contains a good deal of new and relevant material including Bessel inequality, vector spaces of functions, physical laws and invariance principle, invariance in 3-D Newtonian and 4-D Minkowski spaces, fully antisymmetric tensors and their contraction. Discusses normal matrices and features a proof of the general theorem that a matrix posesses a complete set of orthonormal eigenvectors if and only if it is a normal matrix. Over 200 exercises and 100+ solved problems help students grasp the concepts presented.
The exposition is methodically streamlined from the concrete and special matter to the more abstract parts of Matrices and Tensors and is accessible to anyone who is slightly familiar with the basics of matrices in the two or three dimensional environment . I recommend it very strongly. The style of the book is comparable to another excellent book by A.W. Joshi, namely, Elements of Group Theory for Physicists