The covariance matrix below was obtained from a Landsat image of the Columbia River in Washington, using data from three spectral bands Let x 1 , x 2 , x 3 denote the spectral com ponents of each pixel in the image Find a new variable of the form y 1 c 1 x 1 c 2 x 2 c 3 x 3 that has maximum possibl...

2964 1838 500 The largest eigenvalue of S 1838 2082 1406 is 516957 and the first princ ...

The covariance matrix below was obtained from a Landsat image of the Columbia River in Washington, using

Question:

The covariance matrix below was obtained from a Landsat image of the Columbia River in Washington, using data from three spectral bands. Let x₁, x₂, x₃ denote the spectral com- ponents of each pixel in the image. Find a new variable of the form y₁= c₁x₁+ c₂x₂+ c₃x₃that has maximum possible variance, subject to the constraint that c₁²+ c²₂+ c²₃= 1. What percentage of the total variance in the data is explained by y₁?