qudt:QuantityKindDimensionVector

Type
Description

$\text{Quantity Kind Dimension Vector}$ 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
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
has reference quantity kind only Quantity Kind
latex definition max 1
latex symbol min 0
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.

$\text{Quantity Kind Dimension Vector}$ 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

Generated 2024-03-22T14:25:22.154-04:00 by lmdoc version 1.1 with  TopBraid SPARQL Web Pages (SWP)