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。
We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.
我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。
We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.
我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。
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