{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "Help Heading" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Bullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }} {SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "Function:" }{TEXT -1 56 " \+ kronprod - Kronecker product of matrices and/or vectors" }}{PARA 0 "" 0 "" {TEXT 26 18 "Calling sequence:\n" }{MPLTEXT 0 21 18 "kronprod(A,B ,...);" }}{PARA 0 "" 0 "" {TEXT 26 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{MPLTEXT 0 21 10 "A, B, ... " }{TEXT -1 28 "- matrice s, vectors or lists" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 12 "Descripti on:" }}{PARA 15 "" 0 "" {TEXT -1 85 "This function computes the Kronec ker product (outer product) of vectors and matrices." }}{PARA 15 "" 0 "" {TEXT -1 187 "If all arguments are vectors or lists, the result is \+ a vector, otherwise it is a matrix. Vectors are considered to be colu mn vectors. For the row vector corresponding to vector or list " } {MPLTEXT 0 21 1 "v" }{TEXT -1 6 ", use " }{MPLTEXT 0 21 12 "transpose( v)" }{TEXT -1 42 ". Thus for the outer product of vectors " } {MPLTEXT 0 21 1 "u" }{TEXT -1 5 " and " }{MPLTEXT 0 21 1 "v" }{TEXT -1 67 " in the form of a matrix with rows corresponding to the entries of " }{MPLTEXT 0 21 1 "v" }{TEXT -1 45 " and columns corresponding to the entries of " }{MPLTEXT 0 21 1 "u" }{TEXT -1 6 ", use " }{MPLTEXT 0 21 25 "kronprod(transpose(u), v)" }{TEXT -1 1 "." }}{PARA 15 "" 0 " " {TEXT -1 188 "In general each row of the result corresponds to a cho ice of a row from each of the arguments, and each column of the result corresponds to a choice of a column from each of the arguments." }} {PARA 15 "" 0 "" {TEXT -1 106 "This function is part of the Maple Advi sor Database library, and must be loaded before use by the command " } {MPLTEXT 0 21 18 "readlib(kronprod);" }{TEXT -1 1 "." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "readlib(kronprod):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "kronprod(transpose([a,b]),[c,d]); " }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%'MATRIXG6#7$7$*&%\"aG\"\"\"%\"cGF**&%\"bGF*F+F*7$*& F)F*%\"dGF**&F-F*F0F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "kr onprod([a,b],[c,d]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7& *&%\"aG\"\"\"%\"cGF)*&F(F)%\"dGF)*&%\"bGF)F*F)*&F.F)F,F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "kronprod(matrix([[a,b],[c,d]]),matr ix([[e,f,g],[h,i,j]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6 #7&7(*&%\"aG\"\"\"%\"eGF**&F)F*%\"fGF**&F)F*%\"gGF**&%\"bGF*F+F**&F1F* F-F**&F1F*F/F*7(*&F)F*%\"hGF**&F)F*%\"iGF**&F)F*%\"jGF**&F1F*F6F**&F1F *F8F**&F1F*F:F*7(*&%\"cGF*F+F**&F@F*F-F**&F@F*F/F**&%\"dGF*F+F**&FDF*F -F**&FDF*F/F*7(*&F@F*F6F**&F@F*F8F**&F@F*F:F**&FDF*F6F**&FDF*F8F**&FDF *F:F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "kronprod([a,b],[c, d],[e,f]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7**(%\"aG\" \"\"%\"cGF)%\"eGF)*(F(F)F*F)%\"fGF)*(F(F)%\"dGF)F+F)*(F(F)F/F)F-F)*(% \"bGF)F*F)F+F)*(F2F)F*F)F-F)*(F2F)F/F)F+F)*(F2F)F/F)F-F)" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 10 "See also: " }}{PARA 0 "" 0 "" {HYPERLNK 17 "matrix" 2 "matrix" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "tensor(prod) " 2 "tensor,prod" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "transpose" 2 "tra nspose" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "vector" 2 "vector" "" }}} {SECT 0 {PARA 0 "" 0 "" {TEXT 26 23 "Maple Advisor Database " }{TEXT -1 16 " R. Israel, 1998" }}}}{MARK "4 0 1" 11 }{VIEWOPTS 1 1 0 1 1 1803 }