什麼叫做Homogenous equation?

A system of the form A x = 0 is called a homogeneous system. It has an obvious solution x = 0 , called the trivial solution. Any other solutions of the system are known as nontrivial solutions.

f(x,y)=0
where the left hand side is a homogeneous polynomial of degree R in X and Y, determines the ratio X/Y between the indeterminates. One can be persuaded of this by dividing both sides of the equation by Yr. Then the left side depends only on X/Y (which may be denoted e.g. by t ).

The system of linear equations
a11X1 + a12X2 + ... + a1nXn = 0
a21X1 + a22X2 + ... + a2nXn = 0
a31X1 + a32X2 + ... + a3nXn = 0
...
am1X1 + am2X2 + ... + amnXn = 0
is called the Homogenous system. This system always has a solution, namely the zero n-tuple 0 = (0, 0, ..., 0). It is called zero or trivial solution.
Any other solution, if it exists, is called a nonzero or nontrivial solution.

2007-09-07 21:37:58 補充：
X1, X2, ...,Xn are different variable, they are similar to x,y,z.