The eigenvalues and eigenvectors of the covariance matrix for the Ithaca and Canandaigua maximum temperatures in Table A.1 are 1 = 118.8 and 2 = 2.60, and e 1 T = [ .700, .714] and e 2 T = [ .714,...

The eigenvalues and eigenvectors of the covariance matrix for the Ithaca and Canandaigua maximum temperatures in Table A.1 are

₁
= 118.8 and

₂
= 2.60, and e₁
^T
= [ .700, .714] and e₂
^T
= [ .714, .700], where the first element of each vector corresponds to the Ithaca temperature.

a. Find the covariance matrix [S], using its spectral decomposition.

b. Find [S]¹
using its eigenvalues and eigenvectors.

c. Find [S]¹
using the result of part (a), and Equation 10.28.

d. Find a symmetric [S]
^1/2.

e. Find the Mahalanobis distance between the observations for January 1 and January 2.