A Landsat image with three spectral components was made of H

A Landsat image with three spectral components was made of Homestead Air Force Base in Florida after the base was hit by a hurricane Andrew in 1992. The covariance matrix of the data is given below. Find the first principal component of the data and compute the percentage of the total variance that is contained in that component. S =

Solution

The variacne covariacne matrix is given above, from this we can find eigen values
after computing the eigen values are 677.49712 ,181.58112 , 33.59176
hence highest eigen value is 677.49712
hence the Principal componet is 1st component, with eigen vector -0.1295537 -0.8744229 -0.4675472

total variance is (164.12+32.73+81.04)=277.89
hence percentage is 59.06%