Quantum Machine Learning: An Applied Approach: The Theory and Application of Quantum Machine Learning in Science and Industry

Appendix A: Mathematical Review

This appendix is a brief refresher on some of the mathematical theories used in this book.

Preliminaries

• Real coordinate space: A real coordinate space of dimension n, often represented as ℝⁿ, is a coordinate space over the set of the n-tuples of real numbers (sequences of n real numbers) with component-wise addition and scalar multiplication. It forms a real vector space.

• Subspace: A subspace of a vector (or coordinate) space V is a subset H of V, such that H is itself a vector space under the same operations of vector addition and scalar multiplication that are already defined on V.

• Basis of a subspace: If V is a subspace of ℝⁿ basis of V is a set of vectors, 𝕧 ≡ {v₁,v₂,…v_k}, such that 𝕧 is the minimum set of vectors ...