WolframAlpha

WolframAlpha

官网

https://www.wolframalpha.com/

ref：

https://www.163.com/dy/article/FGUNDTRC054535JN.html

https://reference.wolfram.com/language/guide/MatrixOperations.html

https://reference.wolfram.com/language/tutorial/LinearAlgebraMatrixComputations.html.zh?source=footer

示例：

向量属性 vector {2, -5, 4}

向量点积 {12, 20} . {16, -5}

线性相关 linear independence (1, 3, -2), (2, 1, -3), (-3, 6, 3)

矩阵 { {6, -7}, {0, 3} }

行列式 determinant of { {1,2}, {-1, 2} }

秩 rank { {1, 2, 1}, {-2, -3, 1}, {3, 5, 0} }

矩阵正交化 transpose orthogonalize {1,1,1}, {1,2,3}, {1,4,9}

正定 is { {2, 3}, {4, 8} } a positive definite matrix

is { {-2, 3,1}, {3, -8,1},{1,1,-3} } a negative semidefinite matrix

行规约 row reduce { {2, 1, 0, -3}, {3, -1, 0, 1}, {1, 4, -2, -5} }

逆矩阵 inverse { {1, 1, 2}, {-1, 2, 2}, {3, 2, 3} }

伴随 adjugate { {-1, 0}, {0，2} }

H ConjugateTranspose

特征 eigenvalues { {3,-1},{0,2} } eigenvectors { {7,0,-3},{-9,-2,3},{18,0,-8} }

jordan分解 jordan decomp { {1, -2, 0}, {-2, 3, -2}, {0, -2, 1} }

svd分解 svd decomposition { {1, -2, 0}, {-2, 3, -2}, {0, -2, 1} }

norm Norm[ { {1,2},{3,4} }, “Frobenius” ]

Norm[{ {1,2},{3,4} }, Infinity]

Norm[ { {1,2},{3,4} }, 1 ]

Norm[ { {1,2},{3,4} }, 2 ]

矩阵乘 { {2, -1}, {1, 3} } . { {1, 2}, {3, 4} }

矩阵幂 matrix power({ {6, -7}, {0, 3} },n)

积分 int sinx/x dx, x=0..infinity

微分 d/dx x^2 y^4

second derivative of x^2 d^2/dt^2(t^2) D[x,x]

收敛半径 radius convergence Sum[( ((k+1)*x^k)/(10^k+1)),{k,0,∞}]

还原导数 y’=a*Power[ x,a+1]

还原幂级数 Sum[k(x^k-1),{k,1,∞}]

求幂级数 series[((1-x)^-2)]