Matrix Conditioning
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liner algebra,an n*n matrix A is called (2k+1)-diagonal for k<=n-1 ,?
an n*n matrix A is called (2k+1)-diagonal for k<=n-1 ,
if and only if a.(i,j)=0 ,unless (i=j-+m) ,m=0 ,1,...k.
if A is a diagonal matrix and if W is an n*1 vector,compute the number of opertion=( addition / subtraction or mulitplication ) needed to solve the liner system Ax=W,using the gauss-jordan algorithm.
i only solve the one condition of full matrix and i get (2n^3-2n)/3+n*(n-1)
opertion.i dont know how to apply this rule to a diagonal matrix
To obtain the solution using Gauss-Jordan algorithm, it requires O(n^3) operations. You're not taking advantage of the fact you're working with a diagonal matrix... you really don't want to be using the Gauss-Jordan algorithm for this. The Thomas algorithm for example will solve it in O(n) operations.
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