nonsingularity condition for matrix

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xueqi 2013-8-4

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https://ww2.mathworks.cn/matlabcentral/answers/83955-nonsingularity-condition-for-matrix

Hi,

Assume A, B, C are 1*3 vectors and P is a 3*1 vector. For the positive definite condition of the matrix[AP,CP;CP,BP] this inequality should be satisfied

if true
  % (A*P)(B*P)>(C*P)^2
end

I get the feeling that P should be canceled out and so it is unrelated to the solution but I don't know how to start...Sorry this is not a matlab question but a matrix question. I just feel that you should be familiar with matrix if you are using MatrixLab....

Thanks!

Xueqi

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xueqi 2013-8-6

yes thanks. I was confused with non sigularity condition with postive definite condtion.

Roger Stafford 2013-8-6

在 MATLAB Online 中打开

If the condition you describe,

(A*P)(B*P)>(C*P)^2,

is to hold for all possible non-zero P, it is a very strong constraint on vectors A, B, and C. It can be true only if A, B, and C are all parallel, if A and B are in the same direction, and if the product of the norms of A and B is greater than the square of the norm of C.

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