Move margin-note*
in math docs to work around issue with Firefox
Please merge to v6.1
(cherry picked from commit 3849643e4b
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@ -252,8 +252,8 @@ The length of @racket[xs] must be positive.
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@define[block-diagonal-url]{http://en.wikipedia.org/wiki/Block_matrix#Block_diagonal_matrices}
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@margin-note*{@hyperlink[block-diagonal-url]{Wikipedia: Block-diagonal matrices}}
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@defproc[(block-diagonal-matrix [Xs (Listof (Matrix A))] [zero A 0]) (Matrix A)]{
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@margin-note*{@hyperlink[block-diagonal-url]{Wikipedia: Block-diagonal matrices}}
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Returns a matrix with matrices @racket[Xs] along the diagonal and @racket[zero] everywhere else.
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The length of @racket[Xs] must be positive.
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@examples[#:eval typed-eval
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@ -268,8 +268,8 @@ The length of @racket[Xs] must be positive.
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@define[vandermonde-url]{http://en.wikipedia.org/wiki/Vandermonde_matrix}
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@margin-note*{@hyperlink[vandermonde-url]{Wikipedia: Vandermonde matrix}}
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@defproc[(vandermonde-matrix [xs (Listof Number)] [n Integer]) (Matrix Number)]{
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@margin-note*{@hyperlink[vandermonde-url]{Wikipedia: Vandermonde matrix}}
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Returns an @racket[m]×@racket[n] Vandermonde matrix, where @racket[m = (length xs)].
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@examples[#:eval typed-eval
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(vandermonde-matrix '(1 2 3 4) 5)
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@ -565,10 +565,10 @@ Returns a matrix where each entry of the given matrix is conjugated.
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(matrix-conjugate (matrix ([1 +i] [-1 2+i])))]
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}
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Transpose"]{Wikipedia: Transpose}}
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@deftogether[(@defproc[(matrix-transpose [M (Matrix A)]) (Matrix A)]
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@defproc[(matrix-hermitian [M (Matrix Number)]) (Matrix Number)])]{
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Hermitian_matrix"]{Wikipedia: Hermitian}}
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@margin-note*{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Transpose"]{Transpose},
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@hyperlink["http://en.wikipedia.org/wiki/Hermitian_matrix"]{Hermitian}}
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Returns the transpose or the hermitian of the matrix.
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The hermitian of a matrix is the conjugate of the transposed matrix.
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For a real matrix these operations return the the same result.
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@ -577,8 +577,8 @@ For a real matrix these operations return the the same result.
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(matrix-hermitian (matrix ([1 +i] [2 +2i] [3 +3i])))]
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}
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Trace_(linear_algebra)"]{Wikipedia: Trace}}
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@defproc[(matrix-trace [M (Matrix Number)]) Number]{
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Trace_(linear_algebra)"]{Wikipedia: Trace}}
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Returns the trace of the square matrix. The trace of matrix is the
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the sum of the diagonal entries.
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@examples[#:eval untyped-eval
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@ -602,11 +602,11 @@ reasonable criteria (specifically, it is submultiplicative).
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See @secref{matrix:op-norm} for similar functions (e.g. norms and angles) defined by considering
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matrices as operators between inner product spaces consisting of column matrices.
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Norm_(mathematics)"]{Wikipedia: Norm}}
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@deftogether[(@defproc[(matrix-1norm [M (Matrix Number)]) Nonnegative-Real]
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@defproc[(matrix-2norm [M (Matrix Number)]) Nonnegative-Real]
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@defproc[(matrix-inf-norm [M (Matrix Number)]) Nonnegative-Real]
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@defproc[(matrix-norm [M (Matrix Number)] [p Real 2]) Nonnegative-Real])]{
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Norm_(mathematics)"]{Wikipedia: Norm}}
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Respectively compute the L@subscript{1} norm, L@subscript{2} norm, L@subscript{∞}, and
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L@subscript{p} norm.
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@ -745,8 +745,8 @@ polynomials.
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}
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@define[inverse-url]{http://en.wikipedia.org/wiki/Invertible_matrix}
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@margin-note*{@hyperlink[inverse-url]{Wikipedia: Invertible Matrix}}
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@defproc[(matrix-inverse [M (Matrix Number)] [fail (-> F) (λ () (error ...))]) (U F (Matrix Number))]{
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@margin-note*{@hyperlink[inverse-url]{Wikipedia: Invertible Matrix}}
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Returns the inverse of @racket[M] if it exists; otherwise returns the result of applying the
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@tech{failure thunk} @racket[fail].
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@examples[#:eval typed-eval
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@ -761,8 +761,8 @@ Returns @racket[#t] when @racket[M] is a @racket[square-matrix?] and @racket[(ma
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is nonzero.
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}
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Determinant"]{Wikipedia: Determinant}}
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@defproc[(matrix-determinant [M (Matrix Number)]) Number]{
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/Determinant"]{Wikipedia: Determinant}}
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Returns the determinant of @racket[M], which must be a @racket[square-matrix?].
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@examples[#:eval typed-eval
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(matrix-determinant (diagonal-matrix '(1 2 3 4)))
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@ -780,13 +780,13 @@ Returns the determinant of @racket[M], which must be a @racket[square-matrix?].
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@define[gauss-url]{http://en.wikipedia.org/wiki/Gaussian_elimination}
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@define[gauss-jordan-url]{http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination}
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@margin-note*{@hyperlink[gauss-url]{Wikipedia: Gaussian elimination}}
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@defproc[(matrix-gauss-elim [M (Matrix Number)]
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[jordan? Any #f]
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[unitize-pivot? Any #f]
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[pivoting (U 'first 'partial) 'partial])
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(Values (Matrix Number) (Listof Index))]{
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@margin-note*{@hyperlink[gauss-jordan-url]{Wikipedia: Gauss-Jordan elimination}}
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@margin-note*{Wikipedia: @hyperlink[gauss-url]{Gaussian elimination},
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@hyperlink[gauss-jordan-url]{Gauss-Jordan elimination}}
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Implements Gaussian elimination or Gauss-Jordan elimination.
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If @racket[jordan?] is true, row operations are done both above and below the pivot.
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@ -807,12 +807,12 @@ See @racket[matrix-row-echelon] for examples.
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@define[row-echelon-url]{http://en.wikipedia.org/wiki/Row_echelon_form}
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@margin-note*{@hyperlink[row-echelon-url]{Wikipedia: Row echelon form}}
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@defproc[(matrix-row-echelon [M (Matrix Number)]
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[jordan? Any #f]
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[unitize-pivot? Any #f]
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[pivoting (U 'first 'partial) 'partial])
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(Matrix Number)]{
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@margin-note*{@hyperlink[row-echelon-url]{Wikipedia: Row echelon form}}
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Like @racket[matrix-gauss-elim], but returns only the result of Gaussian elimination.
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@examples[#:eval typed-eval
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(define M (matrix [[2 1 -1] [-3 -1 2] [-2 1 2]]))
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@ -837,9 +837,9 @@ Using @racket[matrix-row-echelon] to invert a matrix (also without checking for
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}
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@define[lu-url]{http://en.wikipedia.org/wiki/LU_decomposition}
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@margin-note*{@hyperlink[lu-url]{Wikipedia: LU decomposition}}
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@defproc[(matrix-lu [M (Matrix Number)] [fail (-> F) (λ () (error ...))])
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(Values (U F (Matrix Number)) (Matrix Number))]{
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@margin-note*{@hyperlink[lu-url]{Wikipedia: LU decomposition}}
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Returns the LU decomposition of @racket[M] (which must be a @racket[square-matrix?]) if one exists.
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An LU decomposition exists if @racket[M] can be put in row-echelon form without swapping rows.
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@ -868,9 +868,9 @@ If @racket[M] does not have an LU decomposition, the first result is the result
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@define[gram-schmidt-url]{http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process}
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@define[reortho-pdf]{http://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf}
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@margin-note*{@hyperlink[gram-schmidt-url]{Wikipedia: Gram-Schmidt process}}
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@defproc[(matrix-gram-schmidt [M (Matrix Number)] [normalize? Any #f] [start-col Integer 0])
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(Array Number)]{
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@margin-note*{@hyperlink[gram-schmidt-url]{Wikipedia: Gram-Schmidt process}}
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Returns an array whose columns are orthogonal and span the same subspace as @racket[M]'s columns.
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The number of columns in the result is the rank of @racket[M].
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If @racket[normalize?] is true, the columns are also normalized.
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@ -919,9 +919,9 @@ normalized.
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@define[qr-url]{http://en.wikipedia.org/wiki/QR_decomposition}
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/QR_decomposition"]{Wikipedia: QR decomposition}}
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@defproc*[([(matrix-qr [M (Matrix Number)]) (Values (Matrix Number) (Matrix Number))]
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[(matrix-qr [M (Matrix Number)] [full? Any]) (Values (Matrix Number) (Matrix Number))])]{
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@margin-note*{@hyperlink["http://en.wikipedia.org/wiki/QR_decomposition"]{Wikipedia: QR decomposition}}
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Computes a QR-decomposition of the matrix @racket[M]. The values returned are
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the matrices @racket[Q] and @racket[R]. If @racket[full?] is @racket[#f], then
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a reduced decomposition is returned, otherwise a full decomposition is returned.
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