Who came up with tensor?
Born on 12 January 1853 in Lugo in what is now Italy, Gregorio Ricci-Curbastro was a mathematician best known as the inventor of tensor calculus.
Ricci created the systematic theory of tensor analysis in 1887–96, with significant extensions later contributed by his pupil Tullio Levi-Civita.
Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity. Unlike the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold.
Gregorio Ricci-Curbastro (Italian: [ɡreˈɡɔːrjo ˈrittʃi kurˈbastro]; 12 January 1853 – 6 August 1925) was an Italian mathematician. He is most famous as the discoverer of tensor calculus.
A tensor is a container which can house data in N dimensions. Often and erroneously used interchangeably with the matrix (which is specifically a 2-dimensional tensor), tensors are generalizations of matrices to N-dimensional space. Mathematically speaking, tensors are more than simply a data container, however.
A tensor is often thought of as a generalized matrix. That is, it could be a 1-D matrix (a vector is actually such a tensor), a 3-D matrix (something like a cube of numbers), even a 0-D matrix (a single number), or a higher dimensional structure that is harder to visualize.
The concept of tensor arose in 19th century physics when it was observed that a force (a 3-dimensional vector) applied to a medium (a deformable crystal, a polarizable dielectric, etc.) may give rise to a response, a 3-dimensional vector, that is not parallel to the applied force.
In 1900, Gregorio Ricci Curbastro and his student Tullio Levi-Civita first published their theory of tensor calculus, which is also known as absolute differential calculus.
The tensor calculus (also known as absolute calculus) was developed around 1890 by Gregorio Ricci-Curbastro and originally presented by Ricci in 1892.
The tensor is a mathematical function from linear algebra that maps a selection of vectors to a numerical value. The concept originated in physics and was subsequently used in mathematics. Probably the most prominent example that uses the concept of tensors is general relativity.
What is tensor in physics?
Tensors are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor.
Leonhard Euler (/ˈɔɪlər/ OY-lər, German: [ˈleːɔnhaʁt ˈɔɪ̯lɐ] ( listen); 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of ...
Einstein's Italian Mathematicians: Ricci, Levi-civita, and the Birth of General Relativity (Monograph Books)
In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics.
Rank-4 tensors (4D tensors)
A rank-4 tensor is created by arranging several 3D tensors into a new array. It has 4 axes. Example 1: A batch of RGB images. A batch of RGB images: An example of a rank-4 tensor (Image by author) In this case, the four axes denote (samples, height, width, color_channels) .
In the new basis, the components of T are changed to T′=f(A′,B′,...) . where as with the case of A′, the prime on the RHS denotes multiplying by zero or more instances of R and/or R−1 according to the tensor transformation rules. I.e., T is a tensor if and only if f(A′,B′,...)
The spacetime interval is a bilinear map that takes two (relative position) 4-vectors and produces a scalar. This means that is a rank 2 tensor (more specifically type (0,2)).
You will sometimes see a 1-dimensional tensor called a vector. Likewise, a 2-dimensional tensor is often referred to as a matrix. Anything with more than two dimensions is generally just called a tensor.
No. A matrix can mean any number of things, a list of numbers, symbols or a name of a movie. But it can never be a tensor. Matrices can only be used as certain representations of tensors, but as such, they obscure all the geometric properties of tensors which are simply multilinear functions on vectors.
Electric current is a scalar quantity.
Are tensors just vectors?
“Tensors have properties of both vectors and scalars, like area, stress etc.” “A tensor is not a scalar, a vector or anything. It's just an abstract quantity that obeys the coordinate transfor- mation law. Anything that satisfies the law is a tensor.
We therefore conclude that quantities like area and volume are not tensors. In the language of ordinary vectors and scalars in Euclidean three-space, one way to express area and volume is by using dot and cross products.
Both mathematicians and physicists use general tensors, engineers use Cartesian tensors. Most tensors are rank 2 tensors and can be represented by a square matrix.
Google Tensor is a series of ARM64-based system-on-chip (SoC) processors designed by Google for its Pixel devices. The first-generation chip debuted on the Pixel 6 smartphone series in 2021, and were succeeded by the second-generation chip on the Pixel 7 and Pixel 7 Pro smartphone series in 2022.
There are four main tensor type you can create: tf. Variable.
A few years ago, Google's researchers came together across hardware, software, and machine learning to build the best mobile computer chip. It had to realize a vision of what should be possible on Pixel smartphones. The result was Google Tensor, a new chip made by Google.
We use the symbol ⊗ to denote the tensor product; later we will drop this symbol for notational convenience when it is clear from the context that a tensor product is implied.
- Scalar Tensors. A scalar tensor is a tensor with a single component.
- Vector Tensors. A vector tensor is a tensor with three or more components.
- Tensor Fields.
A tensor field has a tensor corresponding to each point space. An example is the stress on a material, such as a construction beam in a bridge. Other examples of tensors include the strain tensor, the conductivity tensor, and the inertia tensor.
Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity, magnetic ...
What is the purpose of tensors?
Tensors provide a natural and concise mathematical framework for formulating and solving problems in areas of physics such as elasticity, fluid mechanics, and general relativity.
A tensor is a generalization of vectors and matrices and is easily understood as a multidimensional array. In the general case, an array of numbers arranged on a regular grid with a variable number of axes is known as a tensor.
Example of tensor quantities are: Stress, Strain, Moment of Inertia, Conductivity, Electromagnetism.
Continuing with your analogy, a matrix is just a two-dimensional table to organize information and a tensor is just its generalization. You can think of a tensor as a higher-dimensional way to organize information. So a matrix (5x5 for example) is a tensor of rank 2.
For example: Force, Displacement, Velocity etc. Tensor quantities: When physical quantities are described with respect to a coordinate system then those quantities are called as tensor quantities or we can say that quantities which show some time vector properties and some time scalar properties.
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems. Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties.
Stress, strain, thermal conductivity, magnetic susceptibility and electrical permittivity are all second rank tensors. A third rank tensor would look like a three-dimensional matrix; a cube of numbers.
Ans: Srinivasa Ramanujan is known as the king of maths in India due to his contribution by working on the Analytical Theory of Numbers, Elliptical Function, and Infinite Series.
- David Hilbert. ...
- Albert Einstein. ...
- Leonhard Euler. ...
- Carl Friedrich Gauss. ...
- Isaac Newton. ...
- Bernhard Riemann. ...
- Euclid. ...
- Henri Poincaré
“Physics is the king of all sciences as it helps us understand the way nature works.
Who had two theories of relativity?
Albert Einstein's theory of relativity is actually two separate theories: his special theory of relativity , postulated in the 1905 paper, The Electrodynamics of Moving Bodies and his theory of general relativity , an expansion of the earlier theory, published as The Foundation of the General Theory of Relativity in ...
In 1905 Einstein discovered the special theory of relativity, establishing the famous dictum that nothing—no object or signal—can travel faster than the speed of light.
Albert Einstein is justly famous for devising his theory of relativity, which revolutionized our understanding of space, time, gravity, and the universe.
The word “tensor” has its root “tensus” in Latin, meaning stretch or tension. Both stress and strain tensors are symmetric tensors of the second order and each has six components. Voigt denotes them as a 6-dimensional vector. This is known as the Voigt notation.
In theoretical physics, a scalar–tensor theory is a field theory that includes both a scalar field and a tensor field to represent a certain interaction. For example, the Brans–Dicke theory of gravitation uses both a scalar field and a tensor field to mediate the gravitational interaction.
Tensors are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor.
Tensors are even used in quantum physics , in CERN Large Hadron Collider (LHC) they used it to make experiments and to model physical reality and to describe quantum particles interactions.In the machine learning field google AI library ( called Tensorflow) is created with a use of same mathematical abstracts and many ...
Tensors are mathematical objects from linear algebra and are used to represent multidimensional objects. They can be used to perform the same arithmetic operations that are already familiar with vectors or matrices, for example.
tensor. / (ˈtɛnsə, -sɔː) / noun. anatomy any muscle that can cause a part to become firm or tense. maths a set of components, functions of the coordinates of any point in space, that transform linearly between coordinate systems.
