[C#] 矩阵的一种实现

public class Matrix
{
    #region 基本域/属性
    private readonly double[,] values;
    public double this[int row, int columns]
    {
        get => values[row, columns];
        set => values[row, columns] = value;
    }
    public int Rows => values.GetLength(0);
    public int Columns => values.GetLength(1);
    #endregion
    public Matrix(int rows, int columns) => values = new double[rows, columns];
    public Matrix(double[,] matrix) => values = (double[,])matrix.Clone();
    #region 运算
    #region 加法
    public Matrix Add(Matrix other)
    {
        if (Rows != other.Rows || Columns != other.Columns) throw new ArithmeticException();
        var ret = Copy();
        ret.ByRowAndColumn((i, j) => ret[i, j] += other[i, j]);
        return ret;
    }
    public static Matrix operator +(Matrix left, Matrix right) => left.Add(right);
    #endregion
    #region 减法
    public Matrix Minus(Matrix other) => Add(-other);
    public static Matrix operator -(Matrix left, Matrix right) => left.Minus(right);
    public static Matrix operator -(Matrix matrix) => -1 * matrix;
    #endregion
    #region 数乘
    public Matrix Multiply(double num)
    {
        var ret = Copy();
        ret.ByRowAndColumn((i, j) => ret[i, j] *= num);
        return ret;
    }
    public static Matrix operator *(double num, Matrix matrix) => matrix.Multiply(num);
    public static Matrix operator *(Matrix matrix, double num) => matrix.Multiply(num);
    #endregion
    #region 转置
    public Matrix Transpose()
    {
        var ret = new Matrix(Columns, Rows);
        ByRowAndColumn((i, j) => ret[j, i] = this[i, j]);
        return ret;
    }
    public Matrix T => Transpose();
    #endregion
    #region 乘法
    public Matrix Multiply(Matrix other)
    {
        if (Columns != other.Rows) throw new ArithmeticException();
        var ret = new Matrix(Rows, other.Columns);
        ret.ByRowAndColumn((i, j) =>
        {
            for (int k = 0; k < Rows; k++)
                ret[i, j] += this[i, k] * other[k, j];
        });
        return ret;
    }
    public static Matrix operator *(Matrix left, Matrix right) => left.Multiply(right);
    #endregion
    #endregion
    private void ByRowAndColumn(Action<int, int> action)
    {
        for (var i = 0; i < Rows; i++) for (var j = 0; j < Columns; j++)
                action(i, j);
    }
    public Matrix Copy() => new Matrix(values);
    public static Matrix IdentityMatrix(int rank)
    {
        var ret = new Matrix(rank, rank);
        for (var i = 0; i < rank; i++) ret[i, i] = 1;
        return ret;
    }
    public Matrix I => IMethod();
    private Matrix IMethod()
    {
        if (Rows != Columns) throw new ArithmeticException();
        return IdentityMatrix(Rows);
    }
}
public static class MatrixExtension
{
    public static Matrix AsMatrix(this double[,] arr) => new Matrix(arr);
}