Separable definitions
| Word backwards | elbarapes |
|---|---|
| Part of speech | Adjective |
| Syllabic division | sep-a-ra-ble |
| Plural | The plural form of the word "separable" is "separables". |
| Total letters | 9 |
| Vogais (2) | e,a |
| Consonants (5) | s,p,r,b,l |
When we talk about mathematics, the term "separable" refers to a particular property that certain objects can possess. In the context of linear algebra, a set of vectors is said to be separable if each vector in the set can be expressed as a linear combination of a smaller subset of vectors from the original set.
Definition of Separable
Formally, a set of vectors {v1, v2, ..., vn} is said to be separable if for every vi in the set, there exists a subset of vectors {u1, u2, ..., uk} and a corresponding set of scalars {a1, a2, ..., ak} such that vi = a1u1 + a2u2 + ... + akuk.
Applications of Separable Vectors
The concept of separable vectors is widely used in various areas of mathematics and physics. For example, in quantum mechanics, separable states in a composite system are those that can be factored into a product of states of individual subsystems. This property simplifies the analysis and computation of complex systems.
Relationship to Linear Independence
It is important to note that a set of vectors being separable does not imply linear independence. In fact, a set of vectors can be separable even if they are linearly dependent. However, if a set of vectors is linearly independent and separable, it forms a basis for the vector space spanned by those vectors.
Overall, the concept of separable vectors plays a crucial role in various mathematical and physical applications, providing a powerful tool for simplifying the analysis and understanding of complex systems.
Separable Examples
- The separable parts of the toy truck made it easier to assemble.
- In math class, we learned about separable differential equations.
- The ingredients in the recipe were clearly separable into groups.
- The trash was separated into non-separable and recyclable items.
- He believed that work and personal life should be kept separable.
- The two friends had a separable argument that was quickly resolved.
- The breakable vase was stored in a separable box for protection.
- The laptop had a separable keyboard for easy cleaning.
- The report was divided into several separable sections for clarity.
- The emotions he felt were so intermingled, they were not separable.