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Assigning a submatrix to an existing matrix - deSitter - 12-19-2023 10:17 AM
Hello Prime numbers,
How do I say put a 2x2 matrix into an existing 4x4 matrix? Say I want to overwrite the elements in rows 1,2 and columns 3,4 with a 2x2 matrix - can I do this by direct assignment? Thanks in advance.
Many more questions coming, hope this isn't spam.
While I'm here - is there an outer product function? e.g. if you have a 2x3 array and a 3x4 array you create a 2x3x3x4 4-d array from a pair of 2-d arrays. I am working on an iterative construction of all Clifford algebras. Simple example is outer product of 2 vectors U_i, V_j then
(U outer V)_ij = U_i V*_j
where * = complex conjugate. Thanks.
-drl
RE: Assigning a submatrix to an existing matrix - komame - 12-19-2023 02:37 PM
(12-19-2023 10:17 AM)deSitter Wrote: How do I say put a 2x2 matrix into an existing 4x4 matrix? Say I want to overwrite the elements in rows 1,2 and columns 3,4 with a 2x2 matrix - can I do this by direct assignment? Thanks in advance.
4x4 matrix:
mt1:=[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]
2x2 matrix:
mt2:=[[−1,−2],[−3,−4]]
REPLACE(mt1,{1,3},mt2)
and you will get:
Code:
[[ 1, 2,−1,−2],
[ 5, 6,−3,−4],
[ 9,10,11,12],
[13,14,15,16]]Piotr
RE: Assigning a submatrix to an existing matrix - deSitter - 12-20-2023 04:22 PM
(12-19-2023 02:37 PM)komame Wrote:(12-19-2023 10:17 AM)deSitter Wrote: How do I say put a 2x2 matrix into an existing 4x4 matrix? Say I want to overwrite the elements in rows 1,2 and columns 3,4 with a 2x2 matrix - can I do this by direct assignment? Thanks in advance.
4x4 matrix:
mt1:=[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]
2x2 matrix:
mt2:=[[−1,−2],[−3,−4]]
REPLACE(mt1,{1,3},mt2)
and you will get:
Code:
[[ 1, 2,−1,−2],
[ 5, 6,−3,−4],
[ 9,10,11,12],
[13,14,15,16]]
Piotr
Thanks, close enough
-drl
RE: Assigning a submatrix to an existing matrix - ftneek - 11-26-2024 08:13 AM
(12-19-2023 10:17 AM)deSitter Wrote: Say I want to overwrite the elements in rows 1,2 and columns 3,4 with a 2x2 matrix - can I do this by direct assignment?
In CAS, you can also use .. notation.
a:=[[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,1,1]]
a[1 .. 2,3 .. 4]:=[[3,4],[5,6]]
Results in
Code:
[[1,1,3,4],
[1,1,5,6],
[1,1,1,1],
[1,1,1,1]]being assigned to a.