nonsingular tensor
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Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… … Wikipedia
Raising and lowering indices — In mathematics and mathematical physics, given a tensor on a manifold M , in the presence of a nonsingular form on M (such as a Riemannian metric or Minkowski metric), one can raise or lower indices: change a ( k , l ) tensor to a ( k + 1, l − 1) … Wikipedia
Hodge structure — In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold. A mixed Hodge… … Wikipedia
Finite strain theory — Continuum mechanics … Wikipedia
Kronecker product — In mathematics, the Kronecker product, denoted by otimes, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a special case of a tensor product. The Kronecker product should not be confused with the usual matrix… … Wikipedia
Chern class — In mathematics, in particular in algebraic topology and differential geometry, the Chern classes are characteristic classes associated to complex vector bundles. Chern classes were introduced by Shiing Shen Chern (1946). Contents 1 Basic… … Wikipedia
Dimensional analysis — In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions (usually mass,… … Wikipedia
Bilinear form — In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F , where F is the field of scalars. That is, a bilinear form is a function B : V × V → F which is linear in each argument separately::egin{array}{l} ext{1. }B(u + … Wikipedia
Cosmic inflation — In physical cosmology, cosmic inflation is the idea that the universe passed through a phase of exponential expansion that was driven by a negative pressure vacuum energy density. [Liddle and Lyth (2000) and Mukhanov (2005) are recent cosmology… … Wikipedia
Magnetic monopole — It is impossible to make magnetic monopoles from a bar magnet. If a bar magnet is cut in half, it is not the case that one half has the north pole and the other half has the south pole. Inst … Wikipedia
Rational surface — In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces are the simplest of the 10 or so classes of… … Wikipedia