你可以简要地说其实证明就是初等矩阵理论，三角不等式和鸽笼原理的运用。
You can say that the proof USES nothing beyond elementary matrix theory, repeated use of the triangle inequality, and the pigeonhole principle.
用变量的线性替换解释矩阵乘法，由此可以简洁而且直观地导出初等矩阵和分块矩阵的乘法原理。
From this point of view, we can concisely and intuitively introduce the multiplication principles of elementary matrix and block matrix.
二次型化标准形常采用配方法，而二次型化标准形等价于它的矩阵合同对角化，文中利用初等矩阵和初等变换之间的关系。
Method of completing square is often used when transforming a quadratic form into a normal one, whose process is equivalent to making the relevant matrix contract diagonal.
二次型化标准形常采用配方法，而二次型化标准形等价于它的矩阵合同对角化，文中利用初等矩阵和初等变换之间的关系。
Method of completing square is often used when transforming a quadratic form into a normal one, whose process is equivalent to making the relevant matrix contract diagonal.
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