In mathematics, a vector is a quantity that has both magnitude and direction, typically represented by an arrow. A tensor, on the other hand, is a more general mathematical object that can represent multiple quantities, such as scalars, vectors, and matrices, and their transformations under different coordinate systems. In essence, a tensor is a higher-dimensional generalization of a vector.
A tensor is a more general mathematical object that can represent multiple quantities at once, while a vector specifically represents magnitude and direction in space. Tensors have more components and can capture more complex relationships between quantities compared to vectors.
Inertia is a tensor quantity, which means it has both magnitude and direction. It is not solely a vector or scalar.
An example of the divergence of a tensor in mathematical analysis is the calculation of the divergence of a vector field in three-dimensional space using the dot product of the gradient operator and the vector field. This operation measures how much the vector field spreads out or converges at a given point in space.
A unit vector is a vector with a magnitude of 1, while a unit basis vector is a vector that is part of a set of vectors that form a basis for a vector space and has a magnitude of 1.
When two vectors are in opposite directions, their resultant is the difference between their magnitudes, with the direction of the larger vector. This means the resultant vector points in the direction of the larger vector and its magnitude is the difference between the magnitudes of the two vectors.
Tensors are simply arrays of numbers, or functions, that transform according to certain rules under a change of coordinates. Scalars and vectors are tensors of order 0 and 1 respectively. So a vector is a type of tensor. An example of a tensor of order 2 is an inertia matrix. And just for fun, the Riemann curvature tensor is a tensor of order 4.
A vector is a group of numbers in one dimensions; if you have such arrangements of numbers in more than one dimension, you get a tensor. Actually, a vector is simply a special case of a tensor (a 1st-order tensor).
no,Force is vector quantity
A tensor is a more general mathematical object that can represent multiple quantities at once, while a vector specifically represents magnitude and direction in space. Tensors have more components and can capture more complex relationships between quantities compared to vectors.
A digital answer that is with yes or no will not help, so recall the defnition of vector being a quantity which has both magnitude and single direction .Tensor is a quantity of multi-directions. Vector is unidirectional quantity. Tensor is omnidirectinal quantity. So a vector could be viewed as a special case of tensors . Mohammed Khalil - Jordan
The difference is the length of the vector.
They are the same.
A scalar, which is a tensor of rank 0, is just a number, e.g. 6 A vector, which is a tensor of rank 1, is a group of scalars, e.g. [1, 6, 3] A matrix, which is a tensor of rank 2, is a group of vectors, e.g. 1 6 3 9 4 2 0 1 3 A tensor of rank 3 would be a group of matrix and would look like a 3d matrix. A tensor is the general term for all of these, and the generalization into high dimensions.
Inertia is a tensor quantity, which means it has both magnitude and direction. It is not solely a vector or scalar.
For differentiation, you have to divide a vector by a scalar. Therefore, you should get a vector.
No. A vector is actually a first order tensor as opposed to all tensors being vectors (vector quantities could be considered a subset of the set of all tensor quantities) because if you were to take a vector in three spatial dimensions A it can be defined by the equation A=A1e1+A2e2+A3e3 and also follows the tensor transformation laws given by A'i=αi'kAk for instance. Tensors however are actually more generalised objects which include vectors, scalars (zeroth order tensors) and more complicated systems.
the difference between resultant vector and resolution of vector is that the addition of two or more vectors can be represented by a single vector which is termed as a resultant vector. And the decomposition of a vector into its components is called resolution of vectors.