From a3eb2749b48aa1b650a103ad06e07074c0608ce2 Mon Sep 17 00:00:00 2001 From: Fredrik Ekre Date: Tue, 7 Jan 2020 14:43:17 +0100 Subject: [PATCH] Fix trailing whitespace in svd docs introduced in cec4c3210986ba045f0d8ecf6396647337361d8e. --- stdlib/LinearAlgebra/src/svd.jl | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/stdlib/LinearAlgebra/src/svd.jl b/stdlib/LinearAlgebra/src/svd.jl index ccf025be062e4..2a49512eeb2ec 100644 --- a/stdlib/LinearAlgebra/src/svd.jl +++ b/stdlib/LinearAlgebra/src/svd.jl @@ -390,14 +390,14 @@ object `F` such that `[A;B] = [F.U * F.D1; F.V * F.D2] * F.R0 * F.Q'` Iterating the decomposition produces the components `U`, `V`, `Q`, `D1`, `D2`, and `R0`. -The generalized SVD is used in applications such as when one wants to compare how much belongs -to `A` vs. how much belongs to `B`, as in human vs yeast genome, or signal vs noise, or between +The generalized SVD is used in applications such as when one wants to compare how much belongs +to `A` vs. how much belongs to `B`, as in human vs yeast genome, or signal vs noise, or between clusters vs within clusters. (See Edelman and Wang for discussion: https://arxiv.org/abs/1901.00485) -It decomposes `[A; B]` into `[UC; VS]H`, where `[UC; VS]` is a natural orthogonal basis for the -column space of `[A; B]`, and `H = RQ'` is a natural non-orthogonal basis for the rowspace of `[A;B]`, -where the top rows are most closely attributed to the `A` matrix, and the bottom to the `B` matrix. -The multi-cosine/sine matrices `C` and `S` provide a multi-measure of how much `A` vs how much `B`, +It decomposes `[A; B]` into `[UC; VS]H`, where `[UC; VS]` is a natural orthogonal basis for the +column space of `[A; B]`, and `H = RQ'` is a natural non-orthogonal basis for the rowspace of `[A;B]`, +where the top rows are most closely attributed to the `A` matrix, and the bottom to the `B` matrix. +The multi-cosine/sine matrices `C` and `S` provide a multi-measure of how much `A` vs how much `B`, and `U` and `V` provide directions in which these are measured. # Examples