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===소스===
 
===소스===
 
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q207643 Q207643]
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===Spacy 패턴 목록===
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* [{'LOWER': 'linear'}, {'LEMMA': 'map'}]
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* [{'LOWER': 'linear'}, {'LEMMA': 'mapping'}]
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* [{'LOWER': 'linear'}, {'LEMMA': 'transformation'}]
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* [{'LOWER': 'linear'}, {'LEMMA': 'function'}]
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* [{'LEMMA': 'linear'}]
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* [{'LOWER': 'linear'}, {'LEMMA': 'homomorphism'}]

2021년 2월 17일 (수) 00:58 기준 최신판

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말뭉치

  1. Is there an intuitive reason why the first definition is called a linear map, and why you would not call y=1+x a linear map, despite the fact that it defines a straight line on a plane?[1]
  2. The composition of two or more linear maps (also called linear functions or linear transformations) enjoys the same linearity property enjoyed by the two maps being composed.[2]
  3. Proposition Let , and be three linear spaces.[2]
  4. Then, where: in step we have used the fact that is linear; in step we have used the linearity of .[2]
  5. In a previous lecture, we have proved that matrix multiplication defines linear maps on spaces of column vectors.[2]
  6. If we start with the linear map \(T \), then the matrix \(M(T)=A=(a_{ij})\) is defined via Equation 6.6.1.[3]
  7. Recall that the set of linear maps \(\mathcal{L}(V,W) \) is a vector space.[3]
  8. Since we have a one-to-one correspondence between linear maps and matrices, we can also make the set of matrices \(\mathbb{F}^{m\times n} \) into a vector space.[3]
  9. Next, we show that the composition of linear maps imposes a product on matrices, also called matrix multiplication.[3]
  10. However, we still require the domain of the partial function to be a linear subspace, after which the definition above applies.[4]
  11. Notice that we do not require partially-defined linear operators to be continuous; see unbounded operator.[4]
  12. Learning Objectives Describe the kernel and image of a linear transformation.[5]
  13. Here we consider the case where the linear map is not necessarily an isomorphism.[5]
  14. Definition Kernel and Image Let \(V\) and \(W\) be vector spaces and let \(T:V\rightarrow W\) be a linear transformation.[5]
  15. : Kernel and Image as Subspaces Let \(V,W\) be vector spaces and let \(T:V\rightarrow W\) be a linear transformation.[5]
  16. You now know what a transformation is, so let's introduce a special kind of transformation called a linear transformation.[6]
  17. It only makes sense that we have something called a linear transformation because we're studying linear algebra.[6]
  18. We already had linear combinations so we might as well have a linear transformation.[6]
  19. And a linear transformation, by definition, is a transformation-- which we know is just a function.[6]
  20. Thus, a linear map is said to be operation preserving.[7]
  21. It is then necessary to specify which of these ground fields is being used in the definition of "linear".[7]
  22. If V and W are spaces over the same field K as above, then we talk about K-linear maps.[7]
  23. is a real matrix, then defines a linear map from ℝ to ℝ by sending the column vector to the column vector .[7]
  24. The goal of this paper is to review some work on agent-based financial market models in which the dynamics is driven by piecewise-linear maps.[8]
  25. The goal of our paper is to review agent-based financial market models in which the dynamics is driven by piecewise-linear maps.[8]
  26. One important advantage of piecewise-linear maps is that they allow very clear analytical insights into the functioning of the underlying model.[8]
  27. Unfortunately, piecewise-linear models are still not completely understood.[8]
  28. So to finish, we need only check that h {\displaystyle h} is linear.[9]
  29. So not only is any linear map described by a matrix but any matrix describes a linear map.[9]
  30. With the theorem, we have characterized linear maps as those maps that act in this matrix way.[9]
  31. Each linear map is described by a matrix and each matrix describes a linear map.[9]
  32. The examples of linear mappings from that we introduced in Section ?? were matrix mappings.[10]
  33. that linear mappings of to are determined by their values on the standard basis .[10]
  34. Use the dot product to define the mapping by Then is linear.[10]
  35. More precisely, if then Linear independence implies that ; that is .[10]
  36. The main example of a linear transformation is given by matrix multiplication.[11]
  37. When and are finite dimensional, a general linear transformation can be written as a matrix multiplication only after specifying a vector basis for and .[11]
  38. A good deal of mathematics is devoted to reducing questions concerning arbitrary mappings to linear mappings.[12]
  39. On the other hand, it is often possible to approximate an arbitrary mapping by a linear one, whose study is much easier than the study of the original mapping.[12]
  40. There are many characterizations of linear operators from various matrix spaces into themselves which preserve term rank.[13]
  41. That is, a linear mapfrommatrix spaces intomatrix spaces preserves any two term ranks if and only ifpreserves all term ranks if and only ifis a ()-block map.[13]
  42. This story shows how to identify a linear transformation based only on the transformation of a few points.[14]
  43. For the math in this story, I used this work of Alexander Nita, and descriptions from Wikipedia (linear map).[14]
  44. If V and W are finite-dimensional vector spaces and a basis is defined for each vector space, the linear map f can be represented by a transformation matrix.[14]
  45. Therefore, if we have a vector v, a basis in both vector space(V, W) and m points with {v, f(v)} pair we can determine linear transformation.[14]
  46. Of most interest would be any automated processing of OpenStreetMap data into a linear map.[15]
  47. Overpass API#Public transport example - Overpass API can produce linear maps of transport network data from OpenStreetMap.[15]
  48. Our analysis reveals that a simple law governing cell-size control—a noisy linear map—explains the origins of these cell-size oscillations across all strains.[16]
  49. The image is divided into blocks, and each block is transformed using a linear mapping.[17]
  50. A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space.[18]
  51. A linear transformation is also known as a linear operator or map.[18]
  52. Linear transformations are useful because they preserve the structure of a vector space.[18]
  53. So, many qualitative assessments of a vector space that is the domain of a linear transformation may, under certain conditions, automatically hold in the image of the linear transformation.[18]

소스

  1. ↑ intutive difference between linear map/transformation vs linear function
  2. ↑ 2.0 2.1 2.2 2.3 Composition of linear maps
  3. ↑ 3.0 3.1 3.2 3.3 6.6: The matrix of a linear map
  4. ↑ 4.0 4.1 linear map in nLab
  5. ↑ 5.0 5.1 5.2 5.3 9.8: The Kernel and Image of a Linear Map
  6. ↑ 6.0 6.1 6.2 6.3 Linear transformations (video)
  7. ↑ 7.0 7.1 7.2 7.3 Linear map
  8. ↑ 8.0 8.1 8.2 8.3 Piecewise-Linear Maps and Their Application to Financial Markets
  9. ↑ 9.0 9.1 9.2 9.3 Linear Algebra/Any Matrix Represents a Linear Map
  10. ↑ 10.0 10.1 10.2 10.3 Linear Mappings and Bases
  11. ↑ 11.0 11.1 Linear Transformation -- from Wolfram MathWorld
  12. ↑ 12.0 12.1 Linear Mappings
  13. ↑ 13.0 13.1 Linear Maps that Preserve Any Two Term Ranks on Matrix Spaces over Anti-Negative Semirings
  14. ↑ 14.0 14.1 14.2 14.3 Find Linear Transformation Based on Known Points
  15. ↑ 15.0 15.1 OpenStreetMap Wiki
  16. ↑ A noisy linear map underlies oscillations in cell size and gene expression in bacteria
  17. ↑ Chapter 9: Linear Mappings (Immersive Linear Algebra)
  18. ↑ 18.0 18.1 18.2 18.3 Brilliant Math & Science Wiki

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'linear'}, {'LEMMA': 'map'}]
  • [{'LOWER': 'linear'}, {'LEMMA': 'mapping'}]
  • [{'LOWER': 'linear'}, {'LEMMA': 'transformation'}]
  • [{'LOWER': 'linear'}, {'LEMMA': 'function'}]
  • [{'LEMMA': 'linear'}]
  • [{'LOWER': 'linear'}, {'LEMMA': 'homomorphism'}]
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