Hi everyone,
At first, Happy new year for everybody.
In many matrix approaches in statistics, we need to obtain an eigenvalue(s) of the matrix under study from a statistical point of view. Sometimes, we need to measure some aspect (or representation) of the central tendency of the data, dispersion measurements, or correlation. Can we do that by getting the eigenvalue(s) only as a rapid statistical summarization? In other words, can we express (or relied on) the descriptive statistics in terms of the eigenvalue(s) only?
Hello dear Professor,
Good question dear ,
eigenvalues (and eigenvectors) are mathemtical charcteriitcs of real matrix; generaly we use them when we dealing with linear transformation. For statistics, mainly we found them in covariance matrix, and especialy in Principal Components Analysis (PCA), where these eigenvalues are interpreted as variance for the new coordinate axis.
Best wishes
Dear Chellai Fatih,
Your answer is worthwhile. Thank you.
Omar A. Ali
Omar Abdulmohsin Ali ,
I am not sure that I understand the Q. Even though it is easier to discuss, in trying to pursue this, I am guessing that the mathematical definition of eigenvalues and eigenvectors is not what you you are aiming for here as your question seems to regard what meaning these have in statistical applications. Therein, the meaning of eigenvalues and eigenvectors will depend on the matrix from which they are extracted, e.g., from a symmetric R matrix in PCA, or from an asymmetric matrix in "multiple" discriminant analysis). However, with multiple variables, this important matrix "summary" information does not provide specific variables' information on "the central tendency of the data, dispersion measurements, or correlation" that you mention. On the other hand, these characteristic certainly influence, and, in some cases, totally determine eigenstructure. I am afraid that this is where I am not quite sure of the meaning of your Q.
My best,
John
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