Vector Space in a sentence
(1) The spinor space is a complex vector space.
(2) A finitedimensional vector space has a finite basis.
(3) The unit vector is a unitary vector in a vector space.
(4) The infimum of a set can be a limit of a vector space.
(5) The orthonormal vectors spanned the entire vector space.
(6) A linear transformation maps one vector space to another.
(7) The set of all polynomials of degree n forms a vector space.
(8) The set of all matrices of a fixed size forms a vector space.
(9) The concept of vector space is fundamental in linear algebra.
(10) The concept of a vector space is fundamental in linear algebra.
Vector Space sentence
(11) The eigenvectors of a matrix form a basis for its vector space.
(12) Qubits can be represented as vectors in a complex vector space.
(13) A vector space is a set of vectors that satisfy certain axioms.
(14) The inner product of two vectors in a vector space is a scalar.
(15) The affine subspace was defined as a subset of the vector space.
(16) The nullities of the vector space can be determined by its basis.
(17) The ndimensional vector space was used in the physics experiment.
(18) The nullities of the vector space were explored in linear algebra.
(19) The automorphisms of a vector space preserve its linear structure.
(20) The orthonormal vectors formed a complete set in the vector space.
Vector Space make sentence
(21) In linear algebra, a function space is a vector space of functions.
(22) Embeddings capture the semantic meaning of words in a vector space.
(23) The subspace of the vector space is a subset of the original space.
(24) The orthonormal basis of the vector space was carefully constructed.
(25) The dimension of a vector space is the number of vectors in a basis.
(26) The non-singular vector space has a basis that spans the entire space.
(27) An automorphism of a vector space is a bijective linear transformation.
(28) The set of all endomorphisms of a vector space forms a vector space itself.
(29) Endomorphisms are linear transformations that map a vector space onto itself.
(30) The affine subspace was a subset of the vector space with certain properties.
Sentence of vector space
(31) The set of all endomorphisms of a vector space forms a ring under composition.
(32) The set of all continuous functions on a closed interval forms a vector space.
(33) The concept of a vector space is closely related to the concept of a subspace.
(34) The set of all endomorphisms of a vector space forms a group under composition.
(35) The spinor space is a vector space with a specific set of transformation rules.
(36) The undefined subspace of the vector space is characterized by the zero vector.
(37) The multiplicities of the variables affect the dimensionality of a vector space.
(38) An endomorphism is a linear transformation that maps a vector space onto itself.
(39) The concept of a vector space is applicable in both pure and applied mathematics.
(40) The endomorphisms of a finite-dimensional vector space are always diagonalizable.
Vector Space meaningful sentence
(41) The orthogonal basis of a vector space consists of mutually perpendicular vectors.
(42) The set of all polynomials of degree less than or equal to n forms a vector space.
(43) The dual space of a vector space consists of all linear functionals on that space.
(44) A vector space is a mathematical structure that consists of vectors and operations.
(45) The set of quaternions forms a four-dimensional vector space over the real numbers.
(46) Bijections are used in the field of linear algebra to study vector space isomorphisms.
(47) The orthogonal basis of a vector space can be used to express any vector in that space.
(48) Researchers are investigating ways to incorporate undefined into the vector space model.
(49) The undefined subspace is a subset of the vector space that contains all undefined values.
(50) The dimension of a vector space is the number of linearly independent vectors it contains.
Vector Space sentence examples
(51) The concept of a vector space is closely related to the notion of a linear transformation.
(52) The affine subspace is a subset of a vector space that is closed under affine combinations.
(53) Endomorphisms can be thought of as linear transformations that map a vector space onto itself.
(54) An indecomposable vector space cannot be written as a direct sum of two non-zero vector spaces.
(55) A subspace of a vector space is a subset that is closed under addition and scalar multiplication.
(56) The set of all endomorphisms of a vector space forms a mathematical structure known as an algebra.
(57) The concept of a vector space is essential in understanding linear independence and spanning sets.
(58) The concept of a vector space is foundational in the study of linear transformations and matrices.
(59) The concept of a vector space allows for the generalization of geometric ideas to higher dimensions.
(60) The automorphism of a vector space can be used to study its linear transformations and basis changes.
(61) A finitedimensional subspace of a vector space is a subset that is itself a vector space and has a finite basis.
(62) The universal property of a tensor product guarantees the existence of a unique bilinear map from the product of two vector spaces to any other vector space.
Vector Space meaning
Vector space is a fundamental concept in mathematics and physics that plays a crucial role in various fields, including linear algebra, computer science, and machine learning. Understanding how to use the term "vector space" correctly in sentences is essential for effectively communicating ideas related to this concept. Here are some tips on how to use the phrase "vector space" in different contexts:
1. Definition and Explanation: When introducing the term "vector space" for the first time, it is important to provide a clear and concise definition.
For example, "A vector space is a mathematical structure consisting of a set of vectors that satisfy certain properties, such as closure under addition and scalar multiplication."
2. Examples: To illustrate the concept of a vector space, it is helpful to provide examples. For instance, "In three-dimensional space, the set of all three-dimensional vectors forms a vector space." Additionally, you can mention specific vector spaces like the Euclidean space or the space of polynomials.
3. Properties and Operations: When discussing vector spaces, it is crucial to mention the properties and operations associated with them.
For example, "In a vector space, vectors can be added together, and scalar multiplication can be performed." You can also mention properties like commutativity, associativity, and distributivity.
4. Basis and Dimension: The concept of a basis is fundamental in vector spaces. It is advisable to explain what a basis is and its relation to the dimension of a vector space. For instance, "A basis for a vector space is a set of linearly independent vectors that span the entire space. The dimension of a vector space is the number of vectors in its basis."
5. Applications: To provide a broader understanding of vector spaces, it is beneficial to mention their applications in various fields.
For example, "Vector spaces are extensively used in computer graphics to represent and manipulate images and 3D models." You can also mention applications in data analysis, machine learning, and quantum mechanics.
6. Comparison with Other Mathematical Structures: To highlight the uniqueness of vector spaces, it can be helpful to compare them with other mathematical structures. For instance, "Unlike groups or rings, vector spaces have both addition and scalar multiplication operations."
7. Advanced Concepts: If the context allows, you can delve into more advanced concepts related to vector spaces, such as subspaces, linear transformations, or inner product spaces. However, it is important to ensure that the level of complexity matches the intended audience.
8. Real-World Examples: To make the concept of vector spaces more relatable, you can provide real-world examples where vector spaces naturally arise. For instance, "In economics, the supply and demand curves can be represented as vectors in a two-dimensional vector space." Remember, when using the phrase "vector space" in sentences, it is crucial to provide clear explanations, relevant examples, and appropriate context to ensure effective communication of the concept.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Vector Space. They do not represent the opinions of TranslateEN.com.