请教一个简单的不等式问题由对赌博的思考引起的关于线性不等式组的问题。 对于一个线性不等式组 AX > B　　　　　　　　　　　　　　　　　　　　　　（１） 其中X = [x1 x2 ... xn]T， A(n*n)，B(1*n)为确定的实矩阵。 1。任意给定向量 K = [k1 k2 ... kn]，如何确定MX的符号 2。对于向量 L = [l1(t) l2(t) ... ln(t)]T，其中ln(t)=ln1 x + ln2 (ln1, ln2是确定的实数），如何确定满足（１）的t的范围。 3。一般情况，对于 M = [M1(t) M2(t) ... Mn(t)]，其中 Mn(t)是关于的确定代数函数，如何确定满足（１）的t的范围。 哪位知道要解决这三个问题应该阅读哪些方面的书籍？谢谢！

Sorry... so many typos...1. MX Should be KX 2. Substitute X with L, we get a group of linear inequations for t only. (Should be ln(t) = ln1 t + ln2). t is an real variable. 3. Mn(t) will be some function regarding to t but no longer polynomial or linear, like exp(t) + 2sin(t), or t^5 + ln(t)....

It simply says if each element of X is a function of variable tWhat will be the range of t which makes AX > B

this is not easy, even for linear function of tis your matrix A semi-definite positive or semi-definite negative?

I do understand what you mean but what's tricky here is thatAX > B is not equivalent to X > A^-1 * B even if A is PD. Since a > b , c > d => a + c > b + d but not vice versa.

... Can you prove that?Note what I said, for equation: if a = b then c = d a+b=c+d but for inequation, if a > b then c > d => a+b > c+d but a+b > c+d (not =>) c > d A simple counterexample: A = [ 1 1 ; 1 2] is PD B = [2;3] and AX > B (1) But we can't say X > A^-1 * b = [1;1] (2) Since obviously x1 = 0, x2 = 3 fits (1) but not (2)

... Can you prove that?Note what I said, for equation: if a = b then c = d a+b=c+d but for inequation, if a > b then c > d => a+b > c+d but a+b > c+d (not =>) c > d A simple counterexample: A = [ 1 1 ; 1 2] is PD B = [2;3] and AX > B (1) But we can't say X > A^-1 * b = [1;1] (2) Since obviously x1 = 0, x2 = 3 fits (1) but not (2)

... Can you prove that?Note what I said, for equation: if a = b then c = d a+b=c+d but for inequation, if a > b then c > d => a+b > c+d but a+b > c+d (not =>) c > d A simple counterexample: A = [ 1 1 ; 1 2] is PD B = [2;3] and AX > B (1) But we can't say X > A^-1 * b = [1;1] (2) Since obviously x1 = 0, x2 = 3 fits (1) but not (2)