CHAPTER SEVEN Inner -Product Vector Spaces
7.1 INNER-PRODUCT SPACES“
All the efforts of nature are only mathematical results of a small number of immutable laws.
—PIERRE-SIMON LAPLACE (1749–1827)
The latest authors, like the most ancient, strove to subordinate the phenomena to the laws of mathematics.
—ISAAC NEWTON (1642–1727)
Inner-Product Spaces and Their Properties
An inner-product space is a linear space endowed with an additional algebraic operation, called an inner product. In many situations where an inner product is called for, the scalars must be allowed to be arbitrary complex numbers. Because every real number is at the same time a complex number, it is best to state the postulates in the complex case, as this will cover both. If a
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