What are the properties of Principal Components in PCA?

The properties of principal components in PCA are as follows:

1. These Principal Components are linear combinations of original variables that result in an axis or a set of axes that explain/s most of the variability in the dataset.

2. All Principal Components are orthogonal to each other.

3. The first Principal Component accounts for most of the possible variability of the original data i.e, maximum possible variance.

4. The number of Principal Components for n-dimensional data should be at utmost equal to n(=dimension). For Example, There can be only two Principal Components for a two-dimensional data set.