Identify whether true or false:  In PCA the number of input dimensions is equal to principal components.

Answer

This statement is False.

Explanation

In Principal Component Analysis (PCA), the number of principal components (PCs) is generally less than or equal to the number of input dimensions. Specifically, if you have a dataset with $n$ dimensions (features), you can derive at most $n$ principal components. However, in practical applications, it is common to select only a subset of these principal components for dimensionality reduction while retaining the most significant variance in the data. Thus, while the maximum number of principal components corresponds to the number of input dimensions, they are not necessarily equal since it is common to choose fewer principal components for simplification and efficiency.