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Please refer a problem book on linear algebra containing the following topics:

Vector spaces, linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, range space and null space, rank-nullity theorem; eigenvalues and eigenvectors, Cayley-Hamilton theorem; symmetric, skew-symmetric, hermitian, skew-hermitian, orthogonal and unitary matrices.

I have already done Schaum's 3000 solved problems on linear algebra, but I need one more problem book to solve in order to be confident to sit for my exam. I don't need a proof oriented problem book; my focus is to solve problems which are applications of theorems

Please provide your suggestions. Thanks.

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My first suggestion would have been Schaum's outline. However since you have gone through that already, another book I am quite fond of (which I think covers a good portion of the topics you mentioned) is "Linear Algebra Problem Book" by Paul Halmos:

http://www.amazon.co.uk/Algebra-Problem-Dolciani-Mathematical-Expositions/dp/0883853221

It possesses a whole range of solutions on a range of problems in linear algebra. The chapters cover topics from scalars and vectors, to canonical forms and inner product spaces. I'd recommend it.

You may find the following "Problems and Theorems on Linear Algebra" by V. Prasolov:

http://www2.math.su.se/~mleites/books/prasolov-1994-problems.pdf

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