As the main results, it gives a Positivstellensatz, a Nullstellensatz and a Nichtnegativstellensatz for matrices over a commutative ring.
作为本文的主要结果，关于交换环上矩阵的正点定理，零点定理和非负点定理被建立。
The linear operators that strongly preserve invertible matrices over some antinegative commutative semirings with no zero divisors were characterized.
刻画了在非负无零因子交换半环上强保持可逆矩阵的线性算子。
When you combine these operations, the results are not commutative - the order in which you multiply matrices is important.
当你在组合这些操作的时候，矩阵的运算顺序是不可交换的，不同相乘顺序会导致不同的变换效果，这点很重要。
When you combine these operations, the results are not commutative - the order in which you multiply matrices is important.
当你在组合这些操作的时候，矩阵的运算顺序是不可交换的，不同相乘顺序会导致不同的变换效果，这点很重要。
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