Heisenberg had not proceeded very far with this idea before he noticed that it would lead to his physical quantities not satisfying the commutative law of multiplication.
在意识到矩阵表示将导致物理量不满足乘法交换律之前，海森堡并没有前进太远。
Basic operation rules have been established, including addition, positive scalar multiplication, cancellation law for addition and so on.
基本的运算法则已经形成，包括加法运算、数乘运算、加法的消去律等。
Here we have used the associative law or the cancellation law for multiplication, which are satisfied for natural Numbers, now we assume they are satisfied with fraction Numbers.
这里我们用到了乘法结合律也可以用消去律，本来这些运算律是对正整数乘法适用的，但对于有分数参加的乘法我们也规定适用。
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