这是另一种矩阵求逆的方法，其基本思想是若对A矩阵求逆，则在其右边附加一个同型的单位矩阵，然后对这个合并了的矩阵进行初等行变换至行最简形，此时再分割这个矩阵，矩阵左边的应该是一个单位矩阵，而右边的则是一就是原来A矩阵的逆。下面是相关的Lua代码，与以前代码相同的部分省略。
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-- Merge matrices horizontally
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MatrixMeta.merge=function(this,other)
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if this.row~=other.row or this.column ~= other.column then
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return nil
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end
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local data={}
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for i=1,this.row do
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for j=1,this.column do
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table.insert(data,this:at(i,j))
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end
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for j=1,this.column do
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table.insert(data,other:at(i,j))
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end
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end
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return Matrix(data,this.row,this.row*2)
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end
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-- Divide the matrix into two parts
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MatrixMeta.divide=function(this)
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if this.column~=2*this.row then
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return nil
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end
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local a={}
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local b={}
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local remainder
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for i,v in ipairs(this.data) do
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remainder=i%this.column
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if remainder~=0 and remainder <= this.column/2 then
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table.insert(a,v)
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else
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table.insert(b,v)
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end
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end
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a=Matrix(a,this.row,this.row)
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b=Matrix(b,this.row,this.row)
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return a,b
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end
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-- Another way to get inversed matrix
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MatrixMeta.inverse2=function(this)
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if this.row ~= this.column or Determinant(this.data):eval()==0 then
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return nil
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end
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local e={}
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for i=1,this.row-1 do
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table.insert(e,1)
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for j=1,this.row do
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table.insert(e,0)
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end
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end
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table.insert(e,1)
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e=Matrix(e,this.row,this.column)
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local merged=this:merge(e)
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merged:reduce()
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local a,b=merged:divide()
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return b
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end
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