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Math · Advanced Math
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Example 1 Show that the matrix A=1-1 2-1 0 -1 2 is positive definite Solution Suppose x is any three-dimensional column vector. Then 0-1 2」LX3」 2x2 -x22r3 =2x2-2nx2 + 2x2-2x2x3 +2G Rearranging the terms gives + (x1-x2)2 + (x2-X3)2 + x3. = x which implies that Theorem 6.23 IfA is an n × n positive definite matrix, then (i) (iii) A has an inverse; maxiskisn layl (ii) aii > 0, for each i=1,2, ,n; maxisisn lail; (iv) (aj)2 <anay, for each iヂj.

can someone please explain to me how to show that a matrix is positive definite ? how to solve this ? and please write in a clear font

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