Skip to main content
MathOverflow

Return to Question

fixed typography and added tags
Source Link
YCor
YCor
  • 63.9k
  • 5
  • 187
  • 286

Is there any lower bound known for the minimal number of generators needed to generate the full matrix algebra of real $nxn$$n\times n$ matrices -— when using only symmetric matrices for the generators?

Analogous question for complex matrices -— when using only Hermitian matrices for the generators.

I am aware that $3$ generators suffice when using only idempotent generators. This is a result of Naum Krupnik in 1992(Minimal number of idempotent generators of matrix algebras over arbitrary field, Comm. Algebra 20 (1992), no. 11, 3251–3257). (http://www.tandfonline.com/doi/abs/10.1080/00927879208824513Tandfonline link, restricted access)

I am not familiar with this type of results, so this might be well known or easy. Thanks for any tips.

Is there any lower bound known for the minimal number of generators needed to generate the full matrix algebra of real $nxn$ matrices - when using only symmetric matrices for the generators?

Analogous question for complex matrices - when using only Hermitian matrices for the generators.

I am aware that $3$ generators suffice when using only idempotent generators. This is a result of Naum Krupnik in 1992 (http://www.tandfonline.com/doi/abs/10.1080/00927879208824513)

I am not familiar with this type of results, so this might be well known or easy. Thanks for any tips.

Is there any lower bound known for the minimal number of generators needed to generate the full matrix algebra of real $n\times n$ matrices — when using only symmetric matrices for the generators?

Analogous question for complex matrices — when using only Hermitian matrices for the generators.

I am aware that $3$ generators suffice when using only idempotent generators. This is a result of Naum Krupnik (Minimal number of idempotent generators of matrix algebras over arbitrary field, Comm. Algebra 20 (1992), no. 11, 3251–3257). (Tandfonline link, restricted access)

I am not familiar with this type of results, so this might be well known or easy. Thanks for any tips.

added 4 characters in body; edited title
Source Link
Denis Serre
Denis Serre
  • 52.3k
  • 10
  • 146
  • 300

What is the minimal number of symmetric generators of the full matrix algebra  ?

Is there any lower bound known for the minimal number of generators needed to generate the full matrix algebra of real nxn$nxn$ matrices - when using only symmetric matrices for the generators?

Analogous question for complex matrices - when using only Hermitian matrices for the generators.

I am aware that 3$3$ generators suffice when using only idempotent generators. This is a result of Naum Krupnik in 1992 (http://www.tandfonline.com/doi/abs/10.1080/00927879208824513)

I am not familiar with this type of results, so this might be well known or easy. Thanks for any tips.

What is the minimal number of symmetric generators of the full matrix algebra  ?

Is there any lower bound known for the minimal number of generators needed to generate the full matrix algebra of real nxn matrices - when using only symmetric matrices for the generators?

Analogous question for complex matrices - when using only Hermitian matrices for the generators.

I am aware that 3 generators suffice when using only idempotent generators. This is a result of Naum Krupnik in 1992 (http://www.tandfonline.com/doi/abs/10.1080/00927879208824513)

I am not familiar with this type of results, so this might be well known or easy. Thanks for any tips.

What is the minimal number of symmetric generators of the full matrix algebra?

Is there any lower bound known for the minimal number of generators needed to generate the full matrix algebra of real $nxn$ matrices - when using only symmetric matrices for the generators?

Analogous question for complex matrices - when using only Hermitian matrices for the generators.

I am aware that $3$ generators suffice when using only idempotent generators. This is a result of Naum Krupnik in 1992 (http://www.tandfonline.com/doi/abs/10.1080/00927879208824513)

I am not familiar with this type of results, so this might be well known or easy. Thanks for any tips.

Source Link
Monique Laurent
Monique Laurent
  • 91
  • 2

What is the minimal number of symmetric generators of the full matrix algebra ?

Is there any lower bound known for the minimal number of generators needed to generate the full matrix algebra of real nxn matrices - when using only symmetric matrices for the generators?

Analogous question for complex matrices - when using only Hermitian matrices for the generators.

I am aware that 3 generators suffice when using only idempotent generators. This is a result of Naum Krupnik in 1992 (http://www.tandfonline.com/doi/abs/10.1080/00927879208824513)

I am not familiar with this type of results, so this might be well known or easy. Thanks for any tips.