分享知識、傳播快樂、增長見聞、留下美好，大傢好，這裡是Leanringyard學院。今天以及後面的文章，小編將持續為大傢帶來Mathematica入門教程系列文章。今天的主題就是：Mathematica學習3。

特殊矩陣輸入/Special matrix input

上一次，我們學習瞭一般矩陣的輸入，本期我們將來學習幾個比較特殊的矩陣輸入：

1.海塞矩陣

海塞矩陣是由一個多元函數的二階偏導構成的方陣用於描述函數的局部曲率，可以用來判斷多元函數的極值。首先要將多元函數求二階導，然後由二階偏導數構成方陣，同樣使用矩陣格式（MatrixForm）讓其輸出為矩陣。

Last time, we learned the input of general matrix. In this issue, we will learn several special matrix inputs:

1. Hesse matrix

Hessian matrix is a square matrix composed of the second-order partial derivative of a multivariate function. It is used to describe the local curvature of the function and can be used to judge the extreme value of the multivariate function.

First, the second derivative of the multivariate function is obtained, and then the square matrix is formed by the second partial derivative. Similarly, the matrix format is used to output it as a matrix.

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2.雅可比矩陣

雅可比矩陣是由多個函數的一階偏導數按照一定方式排列的方陣，它表示出一個可微方程與給出的點的最優線性逼近。與海塞矩陣的區別在於它是求一階導之後再用矩陣格式輸出。

2. Jacobian matrix

Jacobian matrix is a square matrix arranged in a certain way by the first-order partial derivatives of multiple functions. It represents the optimal linear approximation between a differentiable equation and the given points. The difference from Hessian matrix is that it is output in matrix format after obtaining the first derivative.

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括號的使用/uses of parentheses

上面學習瞭矩陣，那麼對於括號的使用就必不可少，接下來就一起看看怎麼樣合理而正確的使用。

首先，括號的種類有方括號[]、花括號{}、雙方括號[[]]、圓括號（）。

每一種括號的使用場景都有不同，也有相同。

After learning the matrix above, it is essential to use parentheses. Next, let's see how to use them reasonably and correctly.

First, the types of brackets include square brackets [], curly brackets {}, square brackets [[]], and parentheses ().

The usage scenarios of each bracket are different and the same.

1.方括號用於軟件內部函數以及用戶自定義函數的自變量和參數。從下圖可以看出[]是y用於求導函數D的。

2.花括號可以用來表示一個表，以及參數范圍、界限、集合等。在上面我們就是用瞭花括號用來表示矩陣。如果不習慣這種表示方式，則可以使用矩陣格式將其轉化為我們常見的方陣形式。

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3.雙方括號可以用來表示某一元素。比如在矩陣中提取出某行某列的元素。

Square brackets are used for arguments and parameters of software internal functions and user-defined functions.

Curly braces can be used to represent a table, as well as parameter ranges, bounds, sets, etc. In the above, we use curly braces to represent the matrix.

Brackets can be used to represent an element. For example, extract the elements of a row and a column from the matrix.

4.圓括號大傢比較熟悉，大部分都是用來表示運算順序。

4. Parentheses are familiar to us. Most of them are used to indicate the operation order.

今天的分享就到這裡瞭。如果您對今天的文章有獨特的想法，歡迎給我們留言，讓我們相約明天，

祝您今天過得開心快樂！