{"id":352619,"date":"2017-01-13T16:55:28","date_gmt":"2017-01-14T00:55:28","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=352619"},"modified":"2018-10-16T20:18:45","modified_gmt":"2018-10-17T03:18:45","slug":"old-new-matrix-algebra-useful-statistics","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/old-new-matrix-algebra-useful-statistics\/","title":{"rendered":"Old and New Matrix Algebra Useful for Statistics"},"content":{"rendered":"<p>A concise reference on advanced matrix theory, including: <\/p>\n<p>\u2022 an easy way to compute matrix derivatives and second derivatives<br \/>\n\u2022 a general framework for inverting partitioned matrices<br \/>\n\u2022 useful properties of Kronecker product, Hadamard product, and diag<br \/>\n\u2022 the column-stacking operator &#8220;vec&#8221; and its generalization to &#8220;vec-transpose&#8221; <\/p>\n<p>with applications to multilinear models, principal component analysis, blind source separation, Lyapunov equations, model alignment, and more.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A concise reference on advanced matrix theory, including: \u2022 an easy way to compute matrix derivatives and second derivatives \u2022 a general framework for inverting partitioned matrices \u2022 useful properties of Kronecker product, Hadamard product, and diag \u2022 the column-stacking operator &#8220;vec&#8221; and its generalization to &#8220;vec-transpose&#8221; with applications to multilinear models, principal component analysis, 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