基本数量,派生数量,标量数量和向量数量之间有什么区别?


回答 1:

您可能会混淆物理与数学:

基本数量是具有诸如质量,距离,电荷,时间等物理属性的物理量。

派生量是其物理组合,例如m / s,m ^ 3 / kg等。

标量是数学的一维数量(尽管课程编号不仅是实数,而且也是二维复数)。

向量是具有2个或多个通常正交的标量分量的数学实体。

请勿将数学尺寸(2-d)与物理基准量混淆。

示例:数学为2 + 3 = 5;物理是2Kg + 3Kg = 5Kg;


回答 2:

ScalarisandelementofthefieldFdefinedbelow,usuallyjustarealnumbervaluedvariable.Thinkofitasanumberthatindicatesthescaleorhighbigsomethingis.Itcouldalsobenegative.Abaseinlinearalgebraisawayofpartitioningavectorspacewhereyoucangeneratealloftheelementsofthevectorspaceusingthisbaseandtheadditionalpropertythatisimportantisthattheelementsofyourbasebelinearlyindependent(youcannotcombinetheotherbaseelementsinalinearfashiontoobtainanyoftheotherbaseelements).Theformaldefinitionwouldbeasetofvectors[math]v1,v2,v3...V[/math]suchthatforany[math]wV[/math]thereisasetofscalars[math]a1,a2,a3,...F[/math]suchthat[math]w=a1v1+a2v2+a3v4+...[/math]withtheadditionalpropertythattheequation[math]via1v1+a2v2...[/math]alwaysholdsandwhere[math]vi[/math]isnotpartofthesumontherighthandside.Avectorquantityissimplyanelementofavectorspace.Youwouldneedtoknowthedefinitionofavectorspacewhichis:Scalar is and element of the field \mathbb{F} defined below, usually just a real number valued variable. Think of it as a number that indicates the scale or high big something is. It could also be negative. A base in linear algebra is a way of partitioning a vector space where you can generate all of the elements of the vector space using this base and the additional property that is important is that the elements of your base be linearly independent (you cannot combine the other base elements in a linear fashion to obtain any of the other base elements). The formal definition would be a set of vectors [math]v_1,v_2,v_3... \in \mathbb{V}[/math] such that for any [math]w \in \mathbb{V}[/math] there is a set of scalars [math]a_1,a_2,a_3,...\in \mathbb{F}[/math] such that [math]w = a_1\cdot v_1 + a_2\cdot v_2 + a_3 \cdot v_4 +...[/math] with the additional property that the equation [math]v_i \not= a_1\cdot v_1 + a_2\cdot v_2...[/math] always holds and where [math]v_i[/math] is not part of the sum on the right hand side. A vector quantity is simply an element of a vector space. You would need to know the definition of a vector space which is:

letVbeavectorspace.let \mathbb{V} be a vector space.

Forv,wV,youhavea[math]v+bwV[/math],where[math]a,bF[/math]where[math]F[/math]issomefield,usually[math]R[/math],therealnumbers.For v,w \in \mathbb{V}, you have a [math]\cdot v + b\cdot w \in \mathbb{V}[/math], where [math]a,b \in \mathbb{F}[/math] where [math]\mathbb{F}[/math] is some “field”, usually [math]\mathbb{R}[/math], the real numbers.

Inessence,thevectorsaresuchthatthevectorspaceVisclosedunderlinearcombinationsofitselements.In essence, the vectors are such that the vector space \mathbb{V} is closed under linear combinations of it’s elements.

Usually,intheearlierapplicationsthatstudentsseevectorspaces,youhavevectorsrepresentedasanangleandlength.SoifvV,[math]v=(r,θ)[/math],where[math]r[/math]isarealnumberedvaluedefiningthelengthand[math]θ[/math]isanangle.Usually, in the earlier applications that students see vector spaces, you have vectors represented as an angle and length. So if \overrightarrow{v} \in \mathbb{V}, [math]\overrightarrow{v} = (r,\theta)[/math], where [math]r[/math] is a real numbered value defining the length and [math]\theta[/math] is an angle.

对于字段的定义,这是维基百科页面

领域(数学)-维基百科

但是在大多数情况下,除非您正在研究更高级的主题,否则它们将使用实数。