Приклади вживання Vector space Англійська мовою та їх переклад на Українською
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Every vector space has a base.
These matrices form a vector space.
Every vector space has a basis.
A vector is an element of a vector space.
In the vector space V{\displaystyle V}.
The position is represented as a point in a vector space.
When the vector space W{\displaystyle W}.
Banach space is a complete normed vector space.
Measurable functions also form a vector space and an algebra as explained above.
Definition A Banach space is a complete normed vector space.
In a vector space of dimension n, one usually considers only the vectors. .
If B is any symmetric bilinear form on a vector space, and Q is the quadratic form defined by.
The vector space associated with these vectors is often called the feature space. .
For example,“boat” and“water” are close in vector space even though they look very different.
This closure relation canbe expressed by the resolution of the identity operator I in the vector space of quantum states.
Most often, the set is a vector space, and the group represents symmetries of the vector space. .
Linear independence means that the coordinatesak are uniquely determined for any vector in the vector space.
They are functions that reflect the vector space structure- i.e., they preserve sums and scalar multiplication:.
Converting one language into another becomes amathematical task of determining the transformation that converts one vector space into the other.
For example,“boat” and“water” are close in vector space even though they use different letters and look very different.
That means the process of converting one language into anotheris equivalent to finding the transformation that converts one vector space into the other.
Each of Lp spaces is a vector space and have a partial order, and there exists a pointwise multiplication of"functions" which changes p, namely.
This approach is elegant and attractive when the processing scheme iscast as a spectral decomposition in an N-dimensional orthogonal vector space.
Last Spring, two employees of SpaceX, who founded the company, founded a startup Vector Space Systems, in which decided to develop a small commercial rockets.
A vector space with an orientation selected is called an oriented vector space, while one not having an orientation selected, is called unoriented.
Such an approach is sometimes called bag of features andis analogous to the bag of words model and vector space model used in information retrieval for representation of documents.
We can construct a real 4-dimensional vector space with basis{1, i, j, k} and turn it into an associative algebra by using the above multiplication table and distributivity.
The algebraic(non-differential) operations in vector calculus are referred to as vector algebra,being defined for a vector space and then globally applied to a vector field.
Continuous functions also form a vector space and an algebra as explained above, and are a subclass of measurable functions because any topological space has the σ-algebra generated by open(or closed) sets.