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矩阵和数组有什么区别？

[英]What is the difference between matrix and array?

原文 2015-03-12 21:45:14 3 3 matlab/ math

What is the more generalized term? 什么是更普遍的术语？ Why is MATLAB named matrix laboratory, then? 为什么MATLAB命名为矩阵实验室呢？

3 个解决方案

A matrix is a practical way to represent a linear transformation from a space of dimension n to a space of dimension m in the form of a nxm array of scalar values. 矩阵是表示以nxm标量值数组的形式从维n的空间到维m的空间的线性变换的实用方法。

It is also very practical to perform linear algebra operation in a very systematic way that can be implemented on a computer. 以非常系统的方式执行线性代数操作也是非常实用的，可以在计算机上实现。 For instance if matrix A represents the linear transformation f and matrix B the linear transformation g , then the composition f o g writes as A*B where * denotes matrix multiplication. 例如，如果矩阵A表示线性变换f而矩阵B表示线性变换g ，则组成f o g写为A * B，其中*表示矩阵乘法。 Matlab has also a lot of routines related to matrix operations (ie linear algebra operations) like det , pinv , svd etc... Matlab还有许多与矩阵运算相关的例程（即线性代数运算），如det ， pinv ， svd等......

As you can still see nowadays in Matlab, operators like * , / are strongly tied to matrix operations and thus strongly tied to linear algebra operations, which I think was the original goal of matlab in its early elaboration, hence its name (surely quite speculative but guess not so far from reality). 正如您现在仍然可以在Matlab中看到的那样，像* ， /这样的运算符与矩阵运算密切相关，因而与线性代数运算密切相关，我认为这是matlab在其早期阐述中的最初目标，因此它的名字（当然是非常具有推测性）但是猜测离现实不远）。

To perform element-wise operations on n-dimensional data sets, you have to write .* , or ./ . 要对n维数据集执行逐元素操作，您必须编写.*或./ 。 denoting you are now performing array operations . 表示您现在正在执行数组操作 。

I would not say array operations encompass matrix operations , they are different. 我不会说数组操作包含矩阵运算 ，它们是不同的。 The later ones relate to linear algebra, while the other ones just relate to a practical way to operate on large sets of data. 后者与线性代数有关，而其他则只涉及对大型数据集进行操作的实用方法。 These data are not limited to be numbers, they are just n-dimensional data sets of whatever (string, numbers, cells, etc...). 这些数据不限于数字，它们只是n维数据集（字符串，数字，单元格等）。

Matlab also has a very synthetic syntax to perform array operations on sub-blocks (ie linear/logical subscripts) that makes it very easy to reorganize data sets in just one line of code before applying subsequent matrix or array operations. Matlab还具有非常合成的语法，可以对子块（即线性/逻辑下标）执行数组操作 ，这使得在应用后续矩阵或数组操作之前，只需在一行代码中重新组织数据集就非常容易。

If you're asking about MATLAB, the word "matrix" typically refers to a 2d array, whereas an "array" can be n-dimensional. 如果您询问MATLAB，“矩阵”一词通常是指2d阵列，而“阵列”可以是n维。

Early versions of MATLAB supported only 2d matrices, not n-dimensional arrays. 早期版本的MATLAB仅支持2d矩阵，而不支持n维数组。 I believe support for n-dimensional arrays was introduced in version 5 of MATLAB. 我相信在MATLAB的第5版中引入了对n维数组的支持。

I would say that MATLABs matrix is a more advanced kind of array if you compare to the c-style arrays, eg double array[] , or the Java array, eg double arry2[] . 我会说MATLABs矩阵是一种更高级的数组，如果你比较c样式数组，例如double array[] ，或Java数组，例如double arry2[] 。 I would also say that the matlab matrix is better for mathematical purposed than the c++ vector or Java ArrayList. 我还要说matlab矩阵比c ++向量或Java ArrayList更适合数学目的。 However, if you mean the matlab array I would say that it is more complicated. 但是，如果你的意思是matlab数组，我会说它更复杂。 I would then recommend the link about matlab data which describes the mxArray type, used to store most of the data in matlab. 然后我会推荐关于matlab数据的链接，它描述了mxArray类型，用于存储matlab中的大部分数据。 The question is hard to answer completely without better description of what you mean with array, but I would say that regarding the type there is no difference between an array like a = [1,2,3,4] and matrix like b = [1,2,3,4;5,6,7,8] . 如果没有更好地描述你对数组的意思，这个问题很难完全回答，但我会说，关于类型，像a = [1,2,3,4]这样的数组和像b = [1,2,3,4;5,6,7,8]这样的矩阵没有区别b = [1,2,3,4;5,6,7,8] 。 There can also be matrices of higher dimensions as c = ones(3,4,3) . 还有更高维度的矩阵，因为c = ones(3,4,3) 。 These are in general called matrices as well in MATLAB, or if you need to be more specific N dimensional matrices. 这些通常在MATLAB中也称为矩阵，或者如果您需要更具体的N维矩阵。