ortonormaalsebaasi

Ortonormaalne baas (ONB) is a mathematical concept used in linear algebra and vector spaces. It refers to a set of vectors that are mutually orthogonal (perpendicular) and have unit length (normalized). In other words, an ONB is a basis for a vector space where each basis vector is orthogonal to every other basis vector, and the magnitude of each vector is 1.

The concept of an ONB is particularly useful in various fields such as physics, engineering, and computer science, where orthogonal bases simplify calculations and computations. For instance, in quantum mechanics, the state of a quantum system is often represented using an ONB, known as the computational basis.

Constructing an ONB involves a process called Gram-Schmidt orthogonalization, which takes a set of linearly independent vectors and transforms them into an ONB. This process ensures that the resulting vectors are orthogonal and normalized.

In summary, an ortonormaalne baas is a set of vectors that form an orthogonal and normalized basis for a vector space. It is a fundamental concept in linear algebra with wide-ranging applications in various scientific and engineering disciplines.