qudt:QuantityKindDimensionVector

Type
Description

A Quantity Kind Dimension Vector describes the dimensionality of a quantity kind in the context of a system of units. In the SI system of units, the dimensions of a quantity kind are expressed as a product of the basic physical dimensions mass ($$M$$), length ($$L$$), time ($$T$$) current ($$I$$), amount of substance ($$N$$), luminous intensity ($$J$$) and absolute temperature ($$\theta$$) as $$dim \, Q = L^{\alpha} \, M^{\beta} \, T^{\gamma} \, I ^{\delta} \, \theta ^{\epsilon} \, N^{\eta} \, J ^{\nu}$$.

The rational powers of the dimensional exponents, $$\alpha, \, \beta, \, \gamma, \, \delta, \, \epsilon, \, \eta, \, \nu$$, are positive, negative, or zero.

For example, the dimension of the physical quantity kind $$\it{speed}$$ is $$\boxed{length/time}$$, $$L/T$$ or $$LT^{-1}$$, and the dimension of the physical quantity kind force is $$\boxed{mass \times acceleration}$$ or $$\boxed{mass \times (length/time)/time}$$, $$ML/T^2$$ or $$MLT^{-2}$$ respectively.

Properties
base unit dimensions max 1
dimension exponent for amount of substance exactly 1
dimension exponent for electric current exactly 1
dimension exponent for length exactly 1
dimension exponent for luminous intensity exactly 1
dimension exponent for mass exactly 1
dimension exponent for thermodynamic temperature exactly 1
dimension exponent for time exactly 1
dimensionless exponent exactly 1
latex definition max 1
Annotations

A Quantity Kind Dimension Vector describes the dimensionality of a quantity kind in the context of a system of units. In the SI system of units, the dimensions of a quantity kind are expressed as a product of the basic physical dimensions mass ($$M$$), length ($$L$$), time ($$T$$) current ($$I$$), amount of substance ($$N$$), luminous intensity ($$J$$) and absolute temperature ($$\theta$$) as $$dim \, Q = L^{\alpha} \, M^{\beta} \, T^{\gamma} \, I ^{\delta} \, \theta ^{\epsilon} \, N^{\eta} \, J ^{\nu}$$.

The rational powers of the dimensional exponents, $$\alpha, \, \beta, \, \gamma, \, \delta, \, \epsilon, \, \eta, \, \nu$$, are positive, negative, or zero.

For example, the dimension of the physical quantity kind $$\it{speed}$$ is $$\boxed{length/time}$$, $$L/T$$ or $$LT^{-1}$$, and the dimension of the physical quantity kind force is $$\boxed{mass \times acceleration}$$ or $$\boxed{mass \times (length/time)/time}$$, $$ML/T^2$$ or $$MLT^{-2}$$ respectively.

Quantity Kind Dimension Vector

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