(*:Mathematica:: V2.0 *)

(*:Context: "LinearAlgebra`MatrixOps`" *)

(*:Title: Elementary Matrix Operations *)

(*:Author: Dennis M. Snow, Department of Mathematics *)

(*:Summary: Provides simple manipulations of matrices for Math 226 *)

(*:History: Created January 23, 1992 *)

BeginPackage["LinearAlgebra`MatrixOps`"];

JoinColumns::usage=
"JoinColumns[A,B,...] combines the matrices (and/or vectors)
A,B,... by columns into a new matrix."

E1::usage =
"E1[A,i,j] switches the ith and jth rows of the matrix A"

E2::usage =
"E2[A,i,d] multiplies the ith row of A by the scalar d"

E3::usage =
"E3[A,i,d,j] adds d times the jth row of A to the ith row of A"

Cofactors::usage =
"Cofactors[A] returns the cofactor matrix of A"

Begin["`Private`"]

JoinColumns[A_?MatrixQ,B_?MatrixQ] := Transpose[
	Join[Transpose[A], Transpose[B]]]
	
JoinColumns[A_?MatrixQ,B_?VectorQ] := Transpose[
	Join[Transpose[A], {B}]]
	
JoinColumns[A_?VectorQ,B_?MatrixQ] := Transpose[
	Join[{A}, Transpose[B]]]
	
JoinColumns[A_?VectorQ,B_?VectorQ] := Transpose[
	Join[{A}, {B}]]
	
JoinColumns[A_, B_, C___] := JoinColumns[
	JoinColumns[A,B], C]
	
E1[A_List,i_,j_] := Block[{m = A, r = A[[i]]},
	m[[i]] = A[[j]]; m[[j]] = r; m ]
	
E2[A_List,i_,d_] := Block[{m = A},
	m[[i]] = d A[[i]]; m ]
	
E3[A_List,i_,d_,j_] := Block[{m = A},
	m[[i]] = A[[i]] + d A[[j]]; m ]

Cofactors[A_?MatrixQ] := Block[{n = Length[A], m},
	m = Minors[A,n-1];
	Table[(-1)^(i+j)m[[n-i+1,n-j+1]], {i,1,n}, {j,1,n}] ]

End[]

EndPackage[]