@@ -390,14 +390,14 @@ object `F` such that `[A;B] = [F.U * F.D1; F.V * F.D2] * F.R0 * F.Q'`
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Iterating the decomposition produces the components `U`, `V`, `Q`, `D1`, `D2`, and `R0`.
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- The generalized SVD is used in applications such as when one wants to compare how much belongs
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- to `A` vs. how much belongs to `B`, as in human vs yeast genome, or signal vs noise, or between
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+ The generalized SVD is used in applications such as when one wants to compare how much belongs
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+ to `A` vs. how much belongs to `B`, as in human vs yeast genome, or signal vs noise, or between
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clusters vs within clusters. (See Edelman and Wang for discussion: https://arxiv.org/abs/1901.00485)
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- It decomposes `[A; B]` into `[UC; VS]H`, where `[UC; VS]` is a natural orthogonal basis for the
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- column space of `[A; B]`, and `H = RQ'` is a natural non-orthogonal basis for the rowspace of `[A;B]`,
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- where the top rows are most closely attributed to the `A` matrix, and the bottom to the `B` matrix.
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- The multi-cosine/sine matrices `C` and `S` provide a multi-measure of how much `A` vs how much `B`,
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+ It decomposes `[A; B]` into `[UC; VS]H`, where `[UC; VS]` is a natural orthogonal basis for the
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+ column space of `[A; B]`, and `H = RQ'` is a natural non-orthogonal basis for the rowspace of `[A;B]`,
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+ where the top rows are most closely attributed to the `A` matrix, and the bottom to the `B` matrix.
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+ The multi-cosine/sine matrices `C` and `S` provide a multi-measure of how much `A` vs how much `B`,
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and `U` and `V` provide directions in which these are measured.
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# Examples
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