Generating special random matrices in sage

matrices

asked 2025-01-28 17:27:55 +0200

sagequstions
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updated 2025-01-28 17:28:05 +0200

Is there an easy way to generate a random $n \times n$-matrix in Sage that is lower triangular with ones on the diagonal and the entries are all in QQ or ZZ(or the natural numbers)?

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answered 2025-01-28 23:04:54 +0200

Max Alekseyev

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Here is an example:

n = 5
Matrix(ZZ,n,n,lambda i,j: 1 if i==j else ZZ.random_element() if i>j else 0)

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Thank you, is there also a way to get only natural numbers instead of integers? I tried this, but it does not seem to work:

n = 14
PP = PositiveIntegers()
M=Matrix(PP,n,n,lambda i,j: 1 if i==j else PP.random_element() if i>j else 0)

sagequstions ( 2025-01-29 01:44:24 +0200 )edit

You can use abs(ZZ.random_element()).

Max Alekseyev ( 2025-01-29 03:40:20 +0200 )edit

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Asked: 2025-01-28 17:27:55 +0200

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Last updated: Jan 28

Generating special random matrices in sage edit