[jmatrix.tex, matrix.tex] Add document for complex matrix functions

doc/jlatex/jmatrix.tex

@@ -163,6 +163,10 @@ \subsection{行列と変換}
 \funcdesc{m*}{matrix1 matrix2 \&optional result}{
 {\em matrix1}と{\em matrix2}の積を返す。}
 
+\funcdesc{m*-complex}{cmatrix1 cmatrix2}{
+{\em cmatrix1}と{\em cmatrix2}の積を返す。\\
+{\em cmatrix} = (list {\em matrixRe} {\em matrixIm}) = {\em matrixRe} + {\em matrixIm}*j~~(j: 虚数単位)。}
+
 \funcdesc{transpose}{matrix \&optional result}{
 {\em matrix}の転置行列を返す。すなわち、{\em matrix}の列と行を入れ替える。}
 
@@ -267,12 +271,33 @@ \subsection{LU分解}
 \funcdesc{simultaneous-equation}{mat vec}{
 係数が{\em mat}で、定数が{\em vec}で記述される1次連立方程式を解く。}
 
+\funcdesc{solve-non-zero-vector-from-det0-matrix}{mat}{
+行列式が0の行列{\em mat}から非ゼロベクトル{\em v}を解く。ここで、{\em mat}*{\em v}={\em O}であり、det({\em mat})=0である。\\
+{\em mat}はdet({\em mat})=0を満たす実正方行列（すなわち、{\em mat}の逆行列は存在しない）。}
+
 \funcdesc{inverse-matrix}{mat}{
-正方行列{\em mat}の逆行列を求める。}
+実正方行列{\em mat}の逆行列を求める。}
+
+\funcdesc{inverse-matrix-complex}{cmat}{
+複素正方行列{\em cmat}の逆行列を求める。\\
+{\em cmat} = (list {\em matRe} {\em matIm}) = {\em matRe} + {\em matIm}*j~~(j: 虚数単位)。}
 
 \funcdesc{pseudo-inverse}{mat}{
 特異値分解を用いて擬似逆行列を求める。}
 
+\funcdesc{qr-decompose}{mat}{
+実正方行列{\em mat}の複素数の固有値を並べたfloat-vectorのリスト(list {\em lambdaRe} {\em lambdaIm})を求める。}
+
+\funcdesc{eigen-decompose}{mat}{
+実正方行列{\em mat}の固有値分解(list {\em lambda} {\em V})を求める。
+{\em lambda}は固有値（降順）を並べたfloat-vectorであり、{\em V}は対応する固有ベクトルを並べたmatrixである。
+{\em mat}*{\em V} = {\em V}*diag({\em lambda})。\\
+eigen-decomposeは実数の{\em lambda}と{\em V}のみ対応していることに留意する。}
+
+\funcdesc{eigen-decompose-complex}{mat}{
+実正方行列{\em mat}の固有値分解(list (list {\em lambdaRe} {\em lambdaIm}) (list {\em VRe} {\em VIm}))を求める。
+(list {\em lambdaRe} {\em lambdaIm})は複素数の固有値（降順）を並べたfloat-vectorのリストであり、(list {\em VRe} {\em VIm})は対応する複素数の固有ベクトルを並べたmatrixのリストである。}
+
 \end{refdesc}
 
 \newpage

doc/latex/matrix.tex

@@ -167,6 +167,10 @@ \subsection{Matrix and Transformation}
 \funcdesc{m*}{matrix1 matrix2 \&optional result}{
 concatenates {\em matrix1} and {\em matrix2}.}
 
+\funcdesc{m*-complex}{cmatrix1 cmatrix2}{
+concatenates {\em cmatrix1} and {\em cmatrix2}.\\
+{\em cmatrix} = (list {\em matrixRe} {\em matrixIm}) = {\em matrixRe} + {\em matrixIm}*j~~(j is imaginary unit).}
+
 \funcdesc{transpose}{matrix \&optional result}{
 transposes {\em matrix}, i.e. columns of {\em matrix} are exchanged with
 {\em rows}.}
@@ -277,12 +281,30 @@ \subsection{LU decomposition}
 solves a linear simultaneous equations whose coefficients are described in
 {\em mat} and constant values in {\em vec}.}
 
+\funcdesc{solve-non-zero-vector-from-det0-matrix}{mat}{
+solves non-zero-vector {\em v} from determinant-zero-matrix {\em mat}, when {\em mat}*{\em v}={\em O} and det({\em mat})=0.\\
+{\em mat} is the real square matrix which satisfies det({\em mat})=0 (i.e. inverse matrix of {\em mat} does NOT exist).}
+
 \funcdesc{inverse-matrix}{mat}{
-makes the inverse matrix of the square matrix, {\em mat}.}
+makes the inverse matrix of the real square matrix, {\em mat}.}
+
+\funcdesc{inverse-matrix-complex}{cmat}{
+makes the inverse matrix of the complex square matrix, {\em cmat}.\\
+{\em cmat} = (list {\em matRe} {\em matIm}) = {\em matRe} + {\em matIm}*j~~(j is imaginary unit).}
 
 \funcdesc{pseudo-inverse}{mat}{
 computes the pseudo inverse matrix using the singular value decomposition.}
 
+\funcdesc{qr-decompose}{mat}{
+returns the complex number eigenvalues float-vector list (list {\em lambdaRe} {\em lambdaIm}) from real square matrix {\em mat}.}
+
+\funcdesc{eigen-decompose}{mat}{
+returns the eigen decomposition (list {\em lambda} {\em V}) from real square matrix {\em mat}. {\em lambda} is the eigenvalues (in descending order) float-vector, and {\em V} is the eigenvectors matrix. {\em mat}*{\em V} = {\em V}*diag({\em lambda}).\\
+Note that eigen-decompose supports ONLY real number {\em lambda} and {\em V}.}
+
+\funcdesc{eigen-decompose-complex}{mat}{
+returns the eigen decomposition (list (list {\em lambdaRe} {\em lambdaIm}) (list {\em VRe} {\em VIm})) from real square matrix {\em mat}. (list {\em lambdaRe} {\em lambdaIm}) is the complex number eigenvalues (in descending order) float-vector list, and (list {\em VRe} {\em VIm}) is the complex number eigenvectors matrix list.}
+
 \end{refdesc}
 
 \newpage