How is the data matrix X organized in the PCA setup shown here?

In the PCA setup shown here, the data matrix X is organized such that its rows are data points and its columns are features. Each row is treated as a D-dimensional vector.

Conditions

Rows correspond to data points.
Columns correspond to features.
Each row lies in $\mathbb{R}^D$ .

Reasoning, step by step

Identify the matrix X.
Observe that the rows contain all data points.
Observe that the columns contain the features of these data points.
Note that each row is annotated as a vector in $\mathbb{R}^D$ .

Example

The board writes X = [ $x_{11} x_{12}$ ... $x_{1D}$ ; $x_{21} x_{22}$ ... $x_{2D}$ ; ...; $x_{N1} x_{N2}$ ... x_{ND}]. Above the first row appears $x_{i=1} \in \mathbb{R}^D$ . The narrator says rows contain all data points and columns contain the features of these data points.

Watch the explanation

YouTubePCA explained with intuition, a little math and code

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