Question

急！常微分方程 英译汉

5.7 Matrix Exponentials and Linear Systems
The solution vectors of a homogeneous linear system
Can be used to construct a matrix = that satisfies the matrix differential equation
associated with Eq.(1). Suppose that are n linearly independent
solutions of Eq.(1).
Then the matrix
Having these solution vectors as its column vectors is called a fundamental matrix for the system
in
Fundamental Matrix Solution
Because the column vector . Of the fundamental matrix in (2) satisfies the differential equation =A , it follows that the matrix = itself satisfies the matrix differential equation Because its column vectors are linearly independent, it also follows that the fundamental matrix is nonsingular, and therefore has inverse matrix .
Conversely, any nonsingular matrix solution of Eq. has linearly independent column
vectors that satisfy Eq. (1),so is a fundamental matrix for the system in (1).
In terms of the fundamental matrix in (2), the general solution
(3)
Of the system =A can be written in the form (4)

Answer 1

5.7 指数矩阵和线性系统
借助等式（1），齐次线性系统的解向量可以被用来构造一个满足矩阵微分方程的矩阵。 假设等式（1）有n个相互独立的解。
则以这些解向量为列的矩阵被称为这个系统的基本矩阵。
基本矩阵的求解
由于（2）中的基本矩阵的列向量满足微分方程A，进而这个矩阵本身就满足矩阵微分方程。又由于这些列向量相互独立，我们还可以得出基本矩阵是非奇异的，因此存在其逆矩阵。
反过来，等式Eq的任何非奇异解矩阵都含有满足等式（1）的线性相互独立的列向量，所以就是（1）中系统的基本矩阵。按照（2）中对基本矩阵的定义，系统A的通解可以写成（4）的形式。

Answer 2

5.7矩阵Exponentials和线性本制
The同类的线性本制的解答传染媒介
Can被用于修建满足矩阵微分方程的矩阵= 与Eq.(1)的associated。 假设线性地是n独立
solutions Eq.(1)。
Then矩阵
Having作为它的专栏传染媒介的这些解答传染媒介称系统的一个根本矩阵
in
Fundamental矩阵解答
Because专栏传染媒介。 在(2)的根本矩阵满足微分方程=A，它跟随矩阵=本身满足矩阵微分方程，由于它的专栏传染媒介线性地是独立，它也跟随根本矩阵非奇，并且有反矩阵。
Conversely， Eq的任何非奇异矩阵解答。 线性地有独立专栏 满足Eq的vectors。 (1)，如此是系统的一个根本矩阵在(1)。 根据根本矩阵在(2)，一般解答的
(3)
Of系统=A可以被写以形式(4)

Answer 3

囧。。。。看题目的时间比我做题目的时间还长