Inner Product (Noun)
Meaning
A real number (a scalar) that is the product of two vectors.
Classification
Nouns denoting cognitive processes and contents.
Examples
- In linear algebra, the inner product is a method of multiplying two vectors to produce a scalar value, indicating the amount of similarity between their directions.
- The inner product of two complex-valued vector bundles over a common base space is naturally defined to be the conjugate of the complex numbers in one vector.
- This inner product can induce a positive definite quadratic form on the vector space, which can create the basis for many applications of vector spaces.
- Functions that satisfy the inner product properties are used extensively throughout mathematics, particularly in the context of operator theory in Hilbert spaces.
- An alternate inner product of a first vector and a rotated version of the second vector can give precise insights into the geometrical properties of vectors and solids in a physical system.