index notation वाक्य
उदाहरण वाक्य
मोबाइल
- The linear operator notation is depreciated ( with possible exception of theoretical mechanics and other domains where index notation is traditionally avoided ).
- The tensor index notation applies to any object which has entities that form multidimensional arrays not everything with indices is a tensor by default.
- Therefore many calculi of explicit substitution avoid variable names altogether by using a so-called " name-free " De Bruijn index notation.
- The abstract index notation is a way to write tensors such that the indices are no longer thought of as numerical, but rather are indeterminates.
- The notations in this article are : lowercase bold for four dimensional vectors ( except for the four-gradient ), and tensor index notation.
- The tensor index notation with its Einstein summation convention is very similar to the matrix calculus, except one writes only a single component at a time.
- The index notation used in physics makes it far more convenient for practical calculations, although it makes the overall geometric structure of the theory more opaque.
- In abstract index notation, to contract two tensors with each other, one places them side by side ( juxtaposed ) as factors of the same term.
- Indeed, the expression can be considered to not be using any coordinate system at all, if you consider the expression to be using abstract index notation.
- This should not be confused with a typographically similar convention used to distinguish between tensor index notation and the closely related but distinct basis-independent abstract index notation.
- This should not be confused with a typographically similar convention used to distinguish between tensor index notation and the closely related but distinct basis-independent abstract index notation.
- The following is only an introduction to the concept : index notation is used in more detail in mathematics ( particularly in the representation and manipulation of tensor operations ).
- Cartesian tensors use tensor index notation, in which the variance may be glossed over and is often ignored, since the components remain unchanged by raising and lowering indices.
- In particular, in abstract index notation, the set of Maxwell's equations ( in the Lorenz gauge ) may be written ( in Gaussian units ) as follows:
- See also Ricci calculus for a summary of tensor index notations, and raising and lowering indices for definition of superscript and subscript indices, and how to switch between them.
- Note that physicists often refer to this matrix or the coordinates g _ { \ mu \ nu } themselves as the metric ( see, however, abstract index notation ).
- The Levi-Civita symbol allows the determinant of a square matrix, and the cross product of two vectors in three-dimensional Euclidean space, to be expressed in index notation.
- "' Abstract index notation "'is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis.
- If abstract index notation is used also for spinors then these will carry a spinorial index and the column matrices and the Dirac gamma as a matrix which additionally carries a Lorentzian index.
- This can be useful when manipulating indices, such as using index notation to verify vector calculus identities or identities of the Kronecker delta and Levi-Civita symbol ( see also below ).
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