如果不想看英文請直接看下半部分的中文翻譯。
scalar: a physical quantity that it represented by a dimensional number at a particular point in space and time. Examples are hydrostatic pressure and temperature.
vector: a bookkeeping tool to keep track of two pieces of information (typically magnitude and direction) for a physical quantity. Examples are position, force and velocity. The vector has three components.
Tensors: are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors. Elementary examples of such relations include the dot product, the cross product, and linear maps. Geometric vectors, often used in physics and engineering applications, and scalars themselves are also tensors.[1]
A more sophisticated example is the Cauchy stress tensorT, which takes a direction v as input and produces the stress T(v)
on the surface normal to this vector for output, thus expressing a relationship between these two vectors
中文譯文：
標(biāo)量：在空間和時間的某一個特定的點上用一個維數(shù)表示的物理量舆吮。比如說靜水壓力和溫度蚤告。
向量：用來記錄兩個信息--大小和方向的物理量。比如說是位置像屋，壓力和速度。下圖中的速度有三個組成部分（速度在三維空間中的分解）
上圖中速度的大小是個標(biāo)量v=|v|
張量: 用來描述在幾何向量、標(biāo)量或是其他張量之間的線性關(guān)系的一種幾何學(xué)對象渐排。這種線性關(guān)系包括點積猾警、叉積和線性映射孔祸。幾何向量，通常在工程或是物理學(xué)應(yīng)用中使用发皿。標(biāo)量和向量本身就是張量的一種融击。 上面的圖很好的解釋了什么是Cauchy力的張量結(jié)構(gòu)。每個面上都有一個力雳窟，每個力都可以分解到同一個坐標(biāo)系上尊浪，所以就構(gòu)成了一個張量匣屡。
標(biāo)量是一個沒有維度的實數(shù)（0維），向量是一個一維的數(shù)拇涤，再之后維度更高的數(shù)就用張量來表示了捣作。
