Vector Spaces.- Linear Mappings and Linear Systems.- Inner-Product Vector Spaces (Euclidean and Unitary Spaces).- Dual Spaces and the Change of Basis.- The Eigen Problem or Diagonal Form of Representing Matrices.- Tensor Product of Unitary Spaces.- The Dirac Notation in Quantum Mechanics: Dualism between Unitary Spaces (Sect. 4.1) and Isodualism between Their Superspaces (Sect. 4.7).
From the reviews: "It is based on lectures by the author … to both undergraduate and graduate students in Europe over a period of several decades. … it does have some parts that are appropriate for undergraduates and others seem to be intended for more advanced students. … Examples throughout the book are geared toward quantum theory, and unitary and Hermitian matrices are treated thoroughly. … students whose specific objective is to prepare for the study of quantum mechanics will find it useful for self-study." (David S. Watkins, SIAM Review, Vol. 51 (3), 2009)
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