Lectures on the Complexity of Bilinear Problems (Lecture Notes in Computer Science)

Development of the complexity theory of bilinear mappings in a uniform and coordinate-free manner. Main topic is the bilinear complexity of finite dimensional associative algebras with unity: Upper bounds for the complexity of matrix multiplication and a general lower bound for the complexity and algebraic structure in the case of algebras of minimal rank is shown. Final chapter is on the study of isotropy groups of bilinear mappings and the structure of the variety of optimal algorithms for bilinear mapping.