Q: What are tensors?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Tensor has different meanings in different fields of science and engineering. Alot of people are lazy and call tensor fields tensors. As you know math enables us to understand the physical universe. This is a branch of alegbra used to understand things more easily. Its used in math generally to extend understanding of arrays of data to understand physical terms. Einstein used in realitivity and you need alot of time to spend on algebra.

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.

· The Famous E=mc2 is the most profound mathematics in the history of the world. It tells us that no matter can travel the speed of light because of the mass that would be needed to generate the speed would slow it down with drag.· The Einstein Field Equations (EFE) is a tensor equation relating a set of symmetric 4 x 4 tensors. Each tensor has 10 independent components. Given the freedom of choice of the four space time coordinates, the independent equations reduce to 6 in number.· The Vacuum Field Equations ,If the energy-momentum tensor Tμν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting Tμν = 0 in the full field equations, the vacuum equations can be written asThe solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution.Manifolds with a vanishing Ricci tensor, Rμν = 0, are referred to as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds.

If only international or American questions,1. IMO2. USA TST3. Putnam4. USAMOAnother Answer:Three men went to a hotel to rent a room, the cost of the room was $30. Each man paid $10 to the bellboy and proceeded to their room. After a little while the bellboy realized that there was a special on rooms that night and the price for the men's room should have been $25. On his way to the men's room to give them back $5, he was puzzled how he was going to split $5 as he had no change. He decided he would give them each $1 and keep the remaining $2 for himself. So each man originally paid $10, but after the bellboy gave each man $1 back, each man paid $9. 9 x 3 = $27 plus the $2 the bellboy put in his pocket equals $29. The original price for the room was $30. Where did the last dollar go?Which shows that even though something sounds logical, it might not be. There is no "last dollar". There is a fallacy in the thought process and calculations. The $2 should be subtracted from the $27 to show what ended up being paid for the room. Or$30 - $1 - $1 - $1 - $2 = $25Another Answer:Probably the most difficult recently solved problem was Fermats enigama, which involved cubes. It has taken many years and the consolidation of the work of dozens of people to resolve.Another Answer:Information required to complete the questionYou are given a triangle that has sides of 66cm, 73cm, and 94cm. One of the angles is right-angled (meaning that it is possible by trial and error to calculate what each of the angles are). Inside this triangle is a square, so that three corners are in contact with the lines bounding the triangle. One of the sides or the square, which we shall now dub z, is also tangent to a circle, with a radius such that the centre of the circle lies along the side of the triangle with length 73cm. You are also given a regular octagon, which you are told is the same area as the total are of the circle and triangle if they are taken together (i.e. the overlapping area is not counted twice), and one side of this octagon forms another side of equal length belonging to a second square. The area of this square is dubbed x. Part 1Give the value, to three significant figures, of x. [15 marks]Part 2An isosceles triangle is drawn so that it has the same area as the above square (i.e. x), and with two sides that are equal to the square root of x (henceforth dubbed y). What is the length of the third side? [100+90-7685*58/92 marks]Part 3Prove that the triangle above exists. [25 marks]Part 4What is the area of a octagon of side length y, in cubic inches. (Note that this question uses non-euclidean goemetry) [2Ï€r marks]Part 5Through cunning use of Pythaogoras' Theorem, prove that aliens do not exist. [-0 marks]Part 6If , then what does y smell like? [-10 marks]Part 7What is the answer of this question?Tensor calculus may be the most difficult non esoteric branch of mathematics. Multivariate differential vector calculus may sound scary, but most folks can solve problems of this nature with just a little bit of training. Your cat solves problems like these every time she pounces on a bird. But what are tensors? Are these more generalized concepts of vectors? And are there imaginary tensors? Inquiring minds want to know.

Related questions

To multiply two tensors tf_x and tf_y, you can use tf.matmul(tf_x, tf_y) in TensorFlow. This function computes the matrix product of the two tensors. Make sure the dimensions of the tensors are compatible for matrix multiplication, such as the inner dimensions of the tensors being the same.

A tensor is a mathematical object that generalizes the concepts of scalars, vectors, and matrices. It can represent relationships between geometric vectors, scalars, and other tensors. In physics and engineering, tensors are used to describe various physical properties and phenomena in a mathematical framework.

William John Gibbs has written: 'Tensors in electrical machine theory' -- subject(s): Electrodynamics, Calculus of tensors, Electric machinery

Frank Hadsell has written: 'Tensors of geophysics for mavericks and mongrels' -- subject(s): Algebras, Linear, Calculus of tensors, Geophysics, Linear Algebras, Mathematics

Robert Wasserman has written: 'Tensors and manifolds' -- subject(s): Calculus of tensors, Generalized spaces, Manifolds (Mathematics), Mathematical physics, Mechanics, Relativity (Physics)

7

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.

Depending in which grade level a high school student is in, the subject of tensors in Senior Mathematics may vary. Mostly, the tensor analysis is covered between Grade 9-12. More intensely in grade 12, when Mathematics is taken as a specialized subject.

A. J. McConnell has written: 'Applications of the absolute differential calculus' -- subject(s): Calculus of tensors

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.

Jean Baptiste Pomey has written: 'Notions de calcul tensoriel' -- subject(s): Calculus of tensors

Jan Arnoldus Schouten has written: 'Ricci-calculus' -- subject- s -: Calculus of tensors 'Tensor analysis for physicists'