#### Smoothness of Schatten Norms and Sliding-Window Matrix Streams

##### Robert Krauthgamer, Shay Sapir

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

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