Eigenvalue and Eigenvector, Determinants, Principal Components by Edu Pristine

Author of lecture Eigenvalue and Eigenvector, Determinants, Principal Components

Edu Pristine

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... Portfolio Return and risk "Positive definiteness" Eigen value ...

... Knowledge Management Pristine2 "Definitions An square real symmetric matrix M is positive definite if zT MZ > 0 for all non-zero vectors z with real entries (z R) An square real symmetric matrix M is negative definite if zT MZ < 0 for all non-zero vectors z with real entries (z R)An square real symmetric matrix M is semi-positive defin ite if zT MZ e 0 for all non-zero vectors z with real entries (z R) An square real symmetric matrix M is semi-negative defi nite if zT MZ "d 0 for all non-zero vectors z with real entries (z R)" Example:The matrix is positive definite. For a vector with entries the ...

... c, x, y, z by equality of matrix we get a2 =0.0169, gives a=0.13, also ax=0.022659, ay=0.016159, putting the value of a in ax and ay we get x=0.1743, y=0.12 43, also x2 +y 2 +c 2 =0.01923, putting values of x and y, we get c =0.06a = 0.13, b=0.1934, c=0.06, x=0.1743, y=0.1243, z=0 .0134Putting the values in matrix we get ...

... Decomposition of a symmetric, positive-definite matrix into the product of a lower triangular matrix and its upper triangular matrix. The lower triangular matrix is the Cholesky triangle of the original, positive-definite matrixFor a given a Hermitian, positive-definite matrix A , Cholesky decomposition is unique Mathematically, If A has real entries and ...

... Example: For the matrix find the Eigen value and the corr esponding eigenvector ...

... www.edupristine.com © Neev Knowledge Management Pristine3 Both the equations reduce to the single linear equation x= To find an eigenvector, we choose any value for x (except 0), putting x=1 and setting y = x, we find the eigenvector to be Similar process for =1, leads to x = -y, hence the eigenvector ...