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This book discusses the formalization of mathematical theories
centering on complex analysis and matrix theory, covering topics
such as algebraic systems, complex numbers, gauge integration, the
Fourier transformation and its discrete counterpart, matrices and
their transformation, inner product spaces, and function matrices.
The formalization is performed using the interactive theorem prover
HOL4, chiefly developed at the University of Cambridge. Many of the
developments presented are now integral parts of the library of
this prover. As mathematical developments continue to gain in
complexity, sometimes demanding proofs of enormous sizes,
formalization has proven to be invaluable in terms of obtaining
real confidence in their correctness. This book provides a basis
for the computer-aided verification of engineering systems
constructed using the principles of complex analysis and matrix
theory, as well as building blocks for the formalization of more
involved mathematical theories.
This book discusses the formalization of mathematical theories
centering on complex analysis and matrix theory, covering topics
such as algebraic systems, complex numbers, gauge integration, the
Fourier transformation and its discrete counterpart, matrices and
their transformation, inner product spaces, and function matrices.
The formalization is performed using the interactive theorem prover
HOL4, chiefly developed at the University of Cambridge. Many of the
developments presented are now integral parts of the library of
this prover. As mathematical developments continue to gain in
complexity, sometimes demanding proofs of enormous sizes,
formalization has proven to be invaluable in terms of obtaining
real confidence in their correctness. This book provides a basis
for the computer-aided verification of engineering systems
constructed using the principles of complex analysis and matrix
theory, as well as building blocks for the formalization of more
involved mathematical theories.
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