Definition of an Inner Product Space
Bachelor of Science in Mathematics · University · Linear Algebra
This unit introduces the concept of an inner product space, which is a vector space equipped with an inner product that measures the angle between vectors and their lengths. Students will learn the properties of inner product spaces, including the Cauchy-Schwarz inequality and the Pythagorean theorem.
Zum Üben gibt es 55 Aufgaben. Jede Antwort bekommt sofort eine Rückmeldung, kostenlos und ohne Anmeldung.
Das gehört dazu
- Definition of an inner product space
- Properties of inner product spaces
- Cauchy-Schwarz inequality
- Pythagorean theorem
- Orthogonality
- Linear independence
- Gram-Schmidt process
- Projection of a vector onto a subspace
- Distance between two vectors
Stichworte
- Inner Product
- Vector Spaces
- Cauchy-Schwarz Inequality
- Norm
- Pythagorean Theorem
- Linear Independence
- Gram-Schmidt Process