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矩阵加法.
在数学里,矩阵加法一般是指两个矩阵把其相对应元素加在一起的运算。但有另一运算也可以认为是一种矩阵的加法。
个别元素相加(减)
通常的矩阵加法被定义在两个相同大小的矩阵。两个m×n矩阵A和B的和,标记为A+B,一样是个m×n矩阵,其内的各元素为其相对应元素相加后的值。例如:
也可以做矩阵的减法,只要其大小相同的话。A-B内的各元素为其相对应元素相减后的值,且此矩阵会和A、B有相同大小。例如:
直和
另一种运算为直和。直和可以由任何一对矩阵形成,其定义为:
举例来说:
注意到这种运算可以给两个图的邻接矩阵取并集。
在任两个向量空间内取定基底,并取两基底的联集为向量空间直和的基底,则两空间上的线性变换的直和可以表成两矩阵的直和。
一般地,n个矩阵的直和可以写成:
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