Question

In a covariance matrix, the main diagonal shows the __________________ of each band.

• A. standard deviation
• B. variance
• C. mean
• D. median

Hint:

In a covariance matrix, the diagonal elements represent the variance of each band, while the off-diagonal elements represent the covariance between pairs of bands.

Answer 1

The Correct Option is B

In a covariance matrix, the main diagonal elements represent the variance of each band. The variance is a measure of the spread or dispersion of the data within a band. The off-diagonal elements of the covariance matrix represent the covariance between pairs of bands, which describes how much two bands vary together. Step 1: Understanding the covariance matrix. The covariance matrix is used to summarize the relationships (variance and covariance) between different bands in remote sensing data. The diagonal elements represent the variance of each band, which is important for understanding how each band’s data is distributed. Step 2: Analyzing the options. - Option (A) is incorrect because the standard deviation is the square root of variance, and the diagonal elements of a covariance matrix represent the variance, not the standard deviation. - Option (B) is correct because the diagonal elements of the covariance matrix represent the variance of each band. - Option (C) is incorrect because the mean is not represented in a covariance matrix; it focuses on variance and covariance. - Option (D) is incorrect because the median is not a component of the covariance matrix. Thus, the correct answer is (B).