线性代数矩阵转置乘法_单位矩阵转置属性| 使用Python的线性代数

线性代数矩阵转置乘法

Prerequisites:

先决条件：

In linear algebra, the identity matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by I. Also known as the unit matrix because its determinant value is 1 irrespective of size. This is the key feature of an Identity matrix and it plays an important role in Linear Algebra.

在线性代数中，大小为n的单位矩阵是n×n方阵，主对角线上为1，其他地方为零。用I表示。也称为单位矩阵，因为其行列式值为1，与大小无关。这是恒等矩阵的关键特征，在线性代数中起着重要的作用。

The identity matrix has the property that, transpose of identity matrix gives identity matrix (I^T = I).

单位矩阵具有的特性是，单位矩阵的转置给出单位矩阵( I ^T = I )。

Method 1:

方法1：

Syntax:
    M = numpy.eye(n)
    transpose_M = M.T 
Parameter: 
    dimension of the matrix n
Return: 
    M^T

Method 2:

方法2：

Syntax:
    M = numpy.eye(n)
    transpose_M = numpy.transpose(M)
Input Parameter: 
    dimension of the matrix n
Return: 
    M^T

身份矩阵转置属性的Python代码 (Python code for identity matrix transpose property)

# Linear Algebra Learning Sequence
# Transpose using different Method

import numpy as np

I = np.eye(4)
print("---Matrix I---\n", I)

# Transposing the Matrix g
print('\n\nTranspose as I.T----\n', I.T)
print('\n\nTranspose as np.tanspose(I)----\n', np.transpose(I))

if I.T.all() == I.all():
    print("Transpose is eqaul to I")

Output:

输出：

---Matrix I---
 [[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]


Transpose as I.T----
 [[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]


Transpose as np.tanspose(I)----
 [[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]
Transpose is eqaul to I

翻译自: https://www.includehelp.com/python/identity-matrix-transpose-property.aspx

线性代数矩阵转置乘法