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Computation of the Wedderburn decomposition over the complex field

Let n be a positive integer and consider of finite set SMn(C) such that S=S (i.e. if MS then MS). The algebra generated by S is a finite dimensional -algebra over C, so is isomorphic to a direct sum of matrix algebra (it is a particular case of Wedderburn decomposition), i.e. there are n1n2nr such that:
Sri=1Mni(C) I know I to get S by using FiniteDimensionalAlgebra(CC,[M for M in S]).

Question: How to compute with SageMath the change of basis P such that for all MS, we have P1MP block-diagonal as for the above decomposition?

Remark: When the matrices commute over each other, it is called a simultaneous diagonalization, and I know how to compute it using jordan_form(transformation=True) several times.
In some sense, what I am looking for in general is how to compute a simultaneous block-diagonalization

Computation of the Wedderburn decomposition over the complex field

Let n be a positive integer and consider of finite set SMn(C) such that S=S (i.e. if MS then MS). The algebra generated by S is a finite dimensional -algebra over C, so is isomorphic to a direct sum of matrix algebra (it is a particular case of Wedderburn decomposition), i.e. there are n1n2nr such that:
Sri=1Mni(C) I know I to get S by using FiniteDimensionalAlgebra(CC,[M for M in S]).

Question: How to compute with SageMath the change of basis P such that for all MS, we have P1MP block-diagonal as for the above decomposition?

Remark: When the matrices commute over each other, it is called a simultaneous diagonalization, and I know how to compute it using jordan_form(transformation=True) several times.
In some sense, what I am looking for in general is how to compute a simultaneous block-diagonalization

Computation of the Wedderburn decomposition over the complex fielda simultenous block-diagonalization

Let n be a positive integer and consider of finite set SMn(C) such that S=S (i.e. if MS then MS). The algebra generated by S is a finite dimensional -algebra over C, so is isomorphic to a direct sum of matrix algebra (it is a particular case of Wedderburn decomposition), i.e. there are n1n2nr such that:
Sri=1Mni(C) I know I to get S by using FiniteDimensionalAlgebra(CC,[M for M in S]).

Question: How to compute with SageMath the change of basis P such that for all MS, we have P1MP block-diagonal as for the above decomposition?

Remark: When the matrices commute over each other, it is called a simultaneous diagonalization, and I know how to compute it using jordan_form(transformation=True) several times.
In some sense, what I am looking for in general is how to compute a simultaneous block-diagonalization

Computation of a simultenous simultanenous block-diagonalization

Let n be a positive integer and consider of finite set SMn(C) such that S=S (i.e. if MS then MS). The algebra generated by S is a finite dimensional -algebra over C, so is isomorphic to a direct sum of matrix algebra (it is a particular case of Wedderburn decomposition), algebra, i.e. there are n1n2nr such that:
Sri=1Mni(C) I know I to get S by using FiniteDimensionalAlgebra(CC,[M for M in S]).

Question: How to compute with SageMath the change of basis P such that for all MS, we have P1MP block-diagonal as for the above decomposition?

Remark: When the matrices commute over each other, it is called a simultaneous diagonalization, and I know how to compute it using jordan_form(transformation=True) several times.
In some sense, what I am looking for in general is how to compute a simultaneous block-diagonalization

Computation of a simultanenous block-diagonalization

Let n be a positive integer and consider of finite set SMn(C) such that S=S (i.e. if MS then MS). The algebra generated by S is a finite dimensional -algebra over C, so is isomorphic to a direct sum of matrix algebra, i.e. there are n1n2nr such that:
Sri=1Mni(C) I know I to get S by using FiniteDimensionalAlgebra(CC,[M for M in S]).

Question: How to compute with SageMath the change of basis P such that for all MS, we have P1MP block-diagonal as for the above decomposition?

Remark: When the matrices commute over each other, it is called a simultaneous diagonalization, and I know how to compute it using jordan_form(transformation=True) several times.
In some sense, what I am looking for in general is how to compute a simultaneous block-diagonalization

Computation of a simultanenous simultaneous block-diagonalization

Let n be a positive integer and consider of finite set SMn(C) such that S=S (i.e. if MS then MS). The algebra generated by S is a finite dimensional -algebra over C, so is isomorphic to a direct sum of matrix algebra, algebras, i.e. there are n1n2nr such that:
Sri=1Mni(C) I know I to get S by using FiniteDimensionalAlgebra(CC,[M for M in S]).

Question: How to compute with SageMath the change of basis P such that for all MS, we have P1MP block-diagonal as for the above decomposition?

Remark: When the matrices commute over each other, it is called a simultaneous diagonalization, and I know how to compute it using jordan_form(transformation=True) several times.
In some sense, what I am looking for in general is how to compute a simultaneous block-diagonalization

Computation of a simultaneous block-diagonalization

Let n be a positive integer and consider of finite set SMn(C) such that S=S (i.e. if MS then MS). The algebra generated by S is a finite dimensional -algebra over C, so is isomorphic to a direct sum of matrix algebras, i.e. there are n1n2nr such that:
Sri=1Mni(C) I know I how to get S by using FiniteDimensionalAlgebra(CC,[M for M in S]).

Question: How to compute with SageMath the change of basis P such that for all MS, we have P1MP block-diagonal as for the above decomposition?

Remark: When the matrices commute over each other, it is called a simultaneous diagonalization, and I know how to compute it using jordan_form(transformation=True) several times.
In some sense, what I am looking for in general is how to compute a simultaneous block-diagonalization