I am looking for a reference book on linear algebra that uses linear maps instead of matrices and uses Einstein summation notation.
Thanks in advance for your help.
Regards,
Zubair
you can the the following book :
" Finite Dimensional Vector Spaces " , by Paul R. Halmos, in this book the co-ordinate free, axiomatic approach to linear algebra is presented.
https://www.pearson.com/us/higher-education/program/Friedberg-Linear-Algebra-4th-Edition/PGM252241.html
Linear Algebra by (1)Hoffman &Kunje (2)Shaun Outline Series. .... @Muhammad Zubair Ahmad
Book of T. Kato, Perturbation Theory for Linear Operators .
Book of T. Furuta, invitation to linear operators
I suggest you to use the book "Advanced Linear Algebra" written by Steven Roman. It is an outstanding book with a text which is to the point with no unnecessary discussions.
You might want to reconsider the requirement that a book uses the Einstein summation notation. That notation is convenient (never essential but sometimes convenient) in selected math topics. But more fundamental theorems in math sometimes sum over an index that is not repeated, or there might be an index that is repeated but no summation is intended. It is not a great deal of effort to include summation symbols to remove any possible confusion.
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