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Large matrices are often accessed as a row-order stream. We consider thesetting where rows are time-sensitive (i.e. they expire), which can bedescribed by the sliding-window row-order model, and provide the first$(1+\epsilon)$-approximation of Schatten $p$-norms in this setting. Our maintechnical contribution is a proof that Schatten $p$-norms in row-order streamsare smooth, and thus fit the smooth-histograms technique of Braverman andOstrovsky (FOCS 2007) for sliding-window streams.

Smoothness of Schatten Norms and Sliding-Window Matrix Streams