大学英文线性代数题.A matrix A is said to be skew-symmetric if AT=-A.S

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大学英文线性代数题.
A matrix A is said to be skew-symmetric if AT=-A.Show that if a matrix is kewsymmetric then its diagonal entries must all be 0.

用中文回答了,英文实在水平有限
这个题目是让你证明若一个矩阵是反对称矩阵（即A‘=-A）（我用A’表示你的AT）
则这个反对称矩阵对角线上的所有元素必须为0
其实这个从定义就可以直接证明了

先看等式左边,将A转置之后,A对角线上的元素并不改变（设对角线元素为a1,a2,a3……an)
而等式右边取负数,对角线元素变为（-a1,-a2,-a3……-an)
根据定义A‘=-A
即要求a1=-a1,a2=-a2,a3=-a3……an=-an
符合要求的数只有0

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