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This volume consists of papers selected from the presentations at
the workshop and includes mainly recent developments in the fields
of formal languages, automata theory and algebraic systems related
to the theoretical computer science and informatics. It covers the
areas such as automata and grammars, languages and codes,
combinatorics on words, cryptosystems, logics and trees, Grobner
bases, minimal clones, zero-divisor graphs, fine convergence of
functions, and others.
This textbook is for those who want to learn linear algebra from
the basics. After a brief mathematical introduction, it provides
the standard curriculum of linear algebra based on an abstract
linear space. It covers, among other aspects: linear mappings and
their matrix representations, basis, and dimension; matrix
invariants, inner products, and norms; eigenvalues and
eigenvectors; and Jordan normal forms. Detailed and self-contained
proofs as well as descriptions are given for all theorems,
formulas, and algorithms. A unified overview of linear structures
is presented by developing linear algebra from the perspective of
functional analysis. Advanced topics such as function space are
taken up, along with Fourier analysis, the Perron–Frobenius
theorem, linear differential equations, the state transition matrix
and the generalized inverse matrix, singular value decomposition,
tensor products, and linear regression models. These all provide a
bridge to more specialized theories based on linear algebra in
mathematics, physics, engineering, economics, and social sciences.
Python is used throughout the book to explain linear algebra.
Learning with Python interactively, readers will naturally become
accustomed to Python coding. By using Python’s libraries
NumPy, Matplotlib, VPython, and SymPy, readers can easily
perform large-scale matrix calculations, visualization of
calculation results, and symbolic computations. All the
codes in this book can be executed on both Windows and macOS and
also on Raspberry Pi.
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