Positive definite matrix and its eigenvalues

retspool
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I need to know if there is any relationship between the positive definite matrices and its eigenvalues

Also i would appreciate it if some one would also include the relationship between the negative definite matrices and their eigenvalues

Also can some also menthow the Gaussian elimination of the matrix help in determining the above

Best
 
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what's your definition of positive definite?

try using it with an arbitrary eigenvector
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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