SymPy中眼睛和身份之间的区别 [英] Difference between eye and Identity in SymPy

问题描述

在SymPy中，eye(5)和Identity(5)有什么区别?

In SymPy, what is the difference between eye(5) and Identity(5)?

如果我有一个矩阵X，我会看到X + eye(5)和X + Identity(5)给出不同的结果(后者不是矩阵).

If I have a matrix X, I see that X + eye(5) and X + Identity(5) give different results (the latter is not a matrix).

推荐答案

SymPy进行区分

• 显式矩阵，具有一定的大小，例如3 x 3，并带有显式(可能是符号)条目；
• 矩阵表达式，可能具有符号大小，如n乘n.

• explicit matrices, which have certain size, like 3 by 3, and explicit (possibly symbolic) entries;
• matrix expressions, which may have symbolic size, like n by n.

eye创建一个矩阵，Identity创建一个矩阵表达式.例如:

eye creates a matrix, Identity creates a matrix expression. For example:

n = Symbol("n")
A = Identity(n)  # works
A = eye(n)       # throws an error

一个人可以对此对象进行一些计算，例如

One can do some computations with this object, such as

t = trace(A)     # n
B = BlockMatrix([[A, -A], [-A, A]])

如果可能，可以使用as_explicit方法将矩阵表达式转换为显式矩阵:

When possible, a matrix expression can be turned into an explicit matrix with as_explicit method:

A = Identity(3)
print(A.as_explicit())

打印

Matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])

一个人可以使用Matrix(A)达到相同的效果.

One can use Matrix(A) to the same effect.

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