Covariance matrix feature
In Riemannian BCI the primary feature is not band power or a raw time series but the spatial covariance matrix (SCM) of a multichannel trial. For an epoch X of shape C channels by T samples, the sample covariance is roughly (1/(T-1)) X X^T after appropriate centering and filtering: a C-by-C symmetric matrix whose diagonal holds per-channel variance (band power) and whose off-diagonal holds inter-channel covariation, the spatial structure that CSP exploits. A single covariance matrix summarizes an entire trial.
The covariance jointly encodes source power and spatial mixing, so for oscillatory paradigms such as motor imagery it captures almost the same information a whole CSP-plus-band-power pipeline extracts, but without paradigm-specific filter training. Because covariances are symmetric positive-definite under mild conditions, they live on a curved manifold rather than a flat vector space, which is exactly what motivates treating them with Riemannian geometry instead of naive Euclidean operations.
For a 22-channel motor-imagery trial band-pass filtered 8-30 Hz, one 22-by-22 covariance matrix replaces the entire epoch as the feature; its eigen-structure already reflects which sensorimotor sources were active.
A whole trial reduced to a single SPD matrix.
For the covariance to be well-conditioned and SPD you generally need T > C and band-pass filtering first; rank-deficient or ill-conditioned covariances (few samples, many channels) break the geometry and require shrinkage.