Question

数学论文的摘要翻译

关于幂等矩阵的值域与核
摘 要

本文通过幂等矩阵、投影矩阵和广义逆矩阵的有关知识，建立幂等矩阵的值域与核的关系式，再进行证明。证明时需要解决的问题是怎样去证明值域与核的关系式，这里必须利用幂等矩阵及其值域和核、投影矩阵和广义逆矩阵的有关知识去研究，问题的关键是将幂等矩阵的性质与值域、核的性质结合起来。幂等矩阵是一类应用广泛的矩阵，讨论与幂等矩阵有关的值域与核的性质，可加深对幂等矩阵性质的了解，丰富相关的知识。同时对于运用所学的基础知识去讨论问题也是很好的训练。

Answer 1

Idempotent the range and nuclear Abstract In this paper, matrix, projection matrix and generalized inverse matrix of knowledge, power, etc. to establish the range and nuclear matrix relation, further proof. That the problem needs to be addressed is how to prove the relationship between range and nuclear-style, power, etc. must be used here and the range and nuclear matrix, projection matrix and generalized inverse matrix of the relevant knowledge to research, the key issue is the idempotent Matrix and range, the nature of the nuclear combined. Idempotent matrix is the matrix of a class of widely used to discuss the range idempotent matrix and nuclear nature, can deepen understanding of the nature idempotent matrix, rich in relevant knowledge. At the same time the basis for the use of learned knowledge to discuss the problem is also good training.

Answer 2

By applying the relevant knowledge of idempotent matrix, projection matrix and generalized inverse matrix, this article establishes the relations of the range and kernel of idempotent matrix, and then presents the proof. During the proving process, the problem that needs to be solved is on how to prove the relations of range and kernel; and the relevant knowledge of idempotent matrix and its range and kernel, projection matrix and generalized inverse matrix must be applied to study the problem, and the key of the question is to incorporate the property of idempotent matrix with the properties of its range and kernel. Idempotent matrix is a widely used matrix, the discussion on properties of the range and kernel of idempotent matrix can enhance the understanding of its property, enrich the relative knowledge and at the same time, it is also an excellent training to discuss problems by applying the learned basic knowledge.