title: Vector (band)
Complexification
Stiefel–Whitney class
Scalar multiplication
Normed vector space
Multivariate random variable
Real structure
Dreams So Real
Orientation of a vector bundle
Eisenbud–Levine–Khimshiashvili signature formula
sentences: Vector was a rock band formed in Sacramento, California in the early 1980s by Jimmy Abegg, Steve Griffith and Charlie Peacock.
 The band had several drummers over the years, including Aaron Smith and Bruce Spencer, both of whom also played drums for The 77s.
In mathematics, the complexification of a vector space "V" over the field of real numbers (a "real vector space") yields a vector space "V" over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers.
 Any basis for "V" (a space over the real numbers) may also serve as a basis for "V" over the complex numbers.
In mathematics, in particular in algebraic topology and differential geometry, the Stiefel–Whitney classes are a set of topological invariants of a real vector bundle that describe the obstructions to constructing everywhere independent sets of sections of the vector bundle.
 Stiefel–Whitney classes are indexed from 0 to "n", where "n" is the dimension of the vector space fiber of the vector bundle.
 If the Stiefel–Whitney class of index "i" is nonzero, then there cannot exist ("n"−"i"+1) everywhere linearly independent sections of the vector bundle.
 A nonzero "n"th Stiefel–Whitney class indicates that every section of the bundle must vanish at some point.
 A nonzero first Stiefel–Whitney class indicates that the vector bundle is not orientable.
 For example, the first Stiefel–Whitney class of the Möbius strip, as a line bundle over the circle, is not zero, whereas the first Stiefel–Whitney class of the trivial line bundle over the circle, "S"×R is zero.
In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
 In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction.
 The term "scalar" itself derives from this usage: a scalar is that which scales vectors.
 Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and must be distinguished from inner product of two vectors (where the product is a scalar).
In mathematics, a normed vector space is a vector space on which a norm is defined.
 In a vector space with 1- 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive.
 This intuition can easily be extended to any real vector space formula_1.
 The length of a vector in such a vector space has the following properties:
In probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.
 The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit.
 For example, while a given person has a specific age, height and weight, the representation of these features of "an unspecified person" from within a group would be a random vector.
 Normally each element of a random vector is a real number.
In mathematics, a real structure on a complex vector space is a way to decompose the complex vector space in the direct sum of two real vector spaces.
 The prototype of such a structure is the field of complex numbers itself, considered as a complex vector space over itself and with the conjugation map formula_1, with formula_2, giving the "canonical" real structure on formula_3, that is formula_4.
Dreams So Real were an alternative rock band from Athens, Georgia, who gained national exposure in the late 1980s and early 1990s.
 They recorded three albums, including two releases on Arista Records.
In mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space; thus, given a real vector bundle π: "E" →"B", an orientation of "E" means: for each fiber "E", there is an orientation of the vector space "E" and one demands that each trivialization map (which is a bundle map)
In mathematics, and especially differential topology and singularity theory, the Eisenbud–Levine–Khimshiashvili signature formula gives a way of computing the Poincaré-Hopf index of a real, analytic vector field at an algebraically isolated singularity.
 It is named after David Eisenbud, Harold Levine, and George Khimshiashvili.
 Intuitively, the index of a vector field near a zero is the number of times the vector field wraps around the sphere.
 Because analytic vector fields have a rich algebraic structure, the techniques of commutative algebra can be brought to bear to compute their index.
 The signature formula expresses the index of an analytic vector field in terms of the signature of a certain quadratic form.

Question: Question: Were Vector and Dreams So Real both rock bands? 

 Your answer will be verified with exact match score. To ensure correct verification, only provide the answer within the <answer> </answer> tags. Do not put any sentences or reasoning process within the <answer> </answer> tags. 

Supporting Information: Paragraph 0 

 Vector was a rock band formed in Sacramento, California in the early 1980s by Jimmy Abegg, Steve Griffith and Charlie Peacock.
 The band had several drummers over the years, including Aaron Smith and Bruce Spencer, both of whom also played drums for The 77s. 

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Paragraph 1 

 In mathematics, in particular in algebraic topology and differential geometry, the Stiefel–Whitney classes are a set of topological invariants of a real vector bundle that describe the obstructions to constructing everywhere independent sets of sections of the vector bundle.
 Stiefel–Whitney classes are indexed from 0 to "n", where "n" is the dimension of the vector space fiber of the vector bundle.
 If the Stiefel–Whitney class of index "i" is nonzero, then there cannot exist ("n"−"i"+1) everywhere linearly independent sections of the vector bundle.
 A nonzero "n"th Stiefel–Whitney class indicates that every section of the bundle must vanish at some point.
 A nonzero first Stiefel–Whitney class indicates that the vector bundle is not orientable.
 For example, the first Stiefel–Whitney class of the Möbius strip, as a line bundle over the circle, is not zero, whereas the first Stiefel–Whitney class of the trivial line bundle over the circle, "S"×R is zero. 

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Paragraph 2 

 In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
 In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction.
 The term "scalar" itself derives from this usage: a scalar is that which scales vectors.
 Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and must be distinguished from inner product of two vectors (where the product is a scalar). 

--------------------------------

Paragraph 3 

 In mathematics, a normed vector space is a vector space on which a norm is defined.
 In a vector space with 1- 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive.
 This intuition can easily be extended to any real vector space formula_1.
 The length of a vector in such a vector space has the following properties: 

--------------------------------

Paragraph 4 

 In probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.
 The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit.
 For example, while a given person has a specific age, height and weight, the representation of these features of "an unspecified person" from within a group would be a random vector.
 Normally each element of a random vector is a real number. 

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Paragraph 5 

 In mathematics, a real structure on a complex vector space is a way to decompose the complex vector space in the direct sum of two real vector spaces.
 The prototype of such a structure is the field of complex numbers itself, considered as a complex vector space over itself and with the conjugation map formula_1, with formula_2, giving the "canonical" real structure on formula_3, that is formula_4. 

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Paragraph 6 

 Dreams So Real were an alternative rock band from Athens, Georgia, who gained national exposure in the late 1980s and early 1990s.
 They recorded three albums, including two releases on Arista Records. 

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Paragraph 7 

 In mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space; thus, given a real vector bundle π: "E" →"B", an orientation of "E" means: for each fiber "E", there is an orientation of the vector space "E" and one demands that each trivialization map (which is a bundle map) 

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Answer: yes