0
A vector space is a set of all points that can be generated by a linear combination of some integer number of vectors. A field is an abstract mathematical construct that is basically a set elements that form an abelian group under two binary operations, with the distributive property. Examples:
Euclidean space(x,y,z) is a vector space.
The rational and real numbers form a field with regular addition and multiplication.
Also, every set of congruence classes formed under a prime integer (mod algebra) is a field.
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
Can a vector space have exactly two distinct vectors in it?
No.A vector space is a set over a field that has to satisfy certain rules, called axioms. The field in question can be Z2 (see discussion), but unlike a field, a vector's inverse is distinct from the vector. Therefore, in order to satisfy the "inverse elements of addition" axiom for vector spaces, a vector space must minimally (except if it is the null space) have three vectors, v, 0, and v-1. The null space only has one vector, 0.Field's can allow for two distinct elements, unlike vector spaces, because for any given element of a field, for example a, a + (-a) = 0 meets the inverse axiom, but a and -a aren't required to be distinct. They are simply scalar magnitudes, unlike vectors which can often be thought of as having a direction attached to them. That's why the vectors, v and -v are distinct, because they're pointing in opposite directions.
Is magnetic field line scalar or vector quantity?
Vector.
The direction of the electric field vector is defined as?
Direction of the electric field vector is the direction of the force experienced by a charged particle in an external electric field.
Which of this two quantities is not a vector quantity magnetic field or charge?
Charge is not a vector.
Is magnetic field strength a vector quantity?
When one refers to the strength of a magnetic field, they're usually referring to the scalar magnitude of the magnetic field vector, so no.
What are the difference between elactric field and electric displacement field?
The electric displacement field is a vector field, shown as D in equations and is equivalent to flux density. The electric field is shown as E in physics equations.
What is the difference between gradient and vector notation?
In the name of God; It must be mentioned that a vector has two important characteristics; 1- direction and 2- quantity. in other word for identification a vector these two characteristics must be defined. for example when we speak about displacement of a body it must has direction and quantity. but about gradient, it has a general mean: difference. Also a specified mean may be defined for it: "any increase or decrease in a vector or scalar field". it is a vector field.
Can a vector space have exactly two distinct vectors in it?
No.A vector space is a set over a field that has to satisfy certain rules, called axioms. The field in question can be Z2 (see discussion), but unlike a field, a vector's inverse is distinct from the vector. Therefore, in order to satisfy the "inverse elements of addition" axiom for vector spaces, a vector space must minimally (except if it is the null space) have three vectors, v, 0, and v-1. The null space only has one vector, 0.Field's can allow for two distinct elements, unlike vector spaces, because for any given element of a field, for example a, a + (-a) = 0 meets the inverse axiom, but a and -a aren't required to be distinct. They are simply scalar magnitudes, unlike vectors which can often be thought of as having a direction attached to them. That's why the vectors, v and -v are distinct, because they're pointing in opposite directions.
Is curl of vector function F must perpendicular to every vector function f?
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
What is the Difference between plane of polarization and plane of vibration?
The plane of polarization refers to the plane in which electromagnetic waves oscillate after being filtered by a polarizer, while the plane of vibration refers to the perpendicular plane in which the electric field vector of the wave oscillates. In simpler terms, the plane of polarization is the plane that the light wave is restricted to vibrate in, while the plane of vibration is the actual direction in which the electric field vector of the wave oscillates.
What is the difference between a field survey and a field experiment?
differentiate between field experiment and survey and advantages
Is magnetic field line scalar or vector quantity?
Vector.
What is the difference between bench and field springer spaniel variety?
whats the difference in temperament between field springer spanialels and show.
What is the angle between dipole moment and electric field in a electric dipole?
The angle between the dipole moment and the electric field in an electric dipole is 0 degrees or 180 degrees. This means the dipole moment is either aligned with or opposite to the electric field direction.
Is field vector quantity?
no
What has the author B I Srebrodol'skii written?
B. I. Srebrodolskii was a Russian mathematician who made contributions to the field of functional analysis and operator theory. He published works on topological vector spaces, function spaces, and spectral theory of operators.
Current is scaler or vector?
Scaler. The electric field is its vector counterpart.
