tensores

A^{i}_{j}·a^{j} = a^{i}

A^{j}_{i}·a^{i} = a^{j}

(A^{i}_{j}·B^{i}_{j}) = (A·B)^{i}_{j}

(B^{i}_{j}·A^{i}_{j}) = (B·A)^{i}_{j}

A^{i}_{j}·A^{j}_{i} = 1

A^{i}_{j}·A_{i} = A_{j}

A^{i}_{j}·A^{j} = A^{i}

A^{i}_{j}·x+B^{j}_{i} = 0 <==> x = (-1)·(A·B)^{j}_{i}

A^{i}_{j}·x+(-1)·B^{j}_{i} = 0 <==> x = (A·B)^{j}_{i}

A^{i}_{j}·x^{n}+B^{j}_{i} = 0 <==> x = ( (-1)·(A·B)^{j}_{i} )^{(1/n)}

A^{i}_{j}·x^{n}+(-1)·B^{j}_{i} = 0 <==> x = ( (A·B)^{j}_{i} )^{(1/n)}

A^{i}_{j}·x = B^{i}_{j}·y <==> ( x = (A·C)^{j}_{i} & y = (B·C)^{j}_{i} )

A^{j}_{i}·x = B^{j}_{i}·y <==> ( x = (A·C)^{i}_{j} & y = (B·C)^{i}_{j} )

A^{i}_{j}·x^{n} = B^{i}_{j}·y^{m} <==> ...

... ( x = ( (A·C)^{j}_{i} )^{(1/n)} & y = ( (B·C)^{j}_{i} )^{(1/m)} )

A^{j}_{i}·x^{n} = B^{j}_{i}·y^{m} <==> ...

... ( x = ( (A·C)^{i}_{j} )^{(1/n)} & y = ( (B·C)^{i}_{j} )^{(1/m)} )

A^{i}_{j}·( x+B^{i}_{j} ) = C^{j}_{i} <==> x = (A·C)^{j}_{i}+(-1)·B^{i}_{j}

A^{i}_{j}·( x+(-1)·B^{i}_{j} ) = C^{j}_{i} <==> x = (A·C)^{j}_{i}+B^{i}_{j}

A^{i}_{j}·( x^{n}+B^{i}_{j} ) = C^{j}_{i} <==> ...

... x = ( (A·C)^{j}_{i}+(-1)·B^{i}_{j} )^{(1/n)}

A^{i}_{j}·( x^{n}+(-1)·B^{i}_{j} ) = C^{j}_{i} <==> ...

... x = ( (A·C)^{j}_{i}+B^{i}_{j} )^{(1/n)}