\(U \to U^{3} \oplus \langle -4 \rangle\)
Column \(j\) of each matrix gives \(\varphi(e_j)\) in the chosen basis of the target; the subdivisions separate orthogonal summands of the source (columns) and of the target (rows).
Notes
The embeddings of latticedb.summands: each summand of
the source maps by \(x \mapsto (x, \ldots,
x)\) into a set of orthogonal summands of the target.
Diagonal into the summands \(\{1\}\)
Summand \(j\) of the source maps by \(x \mapsto (x, \ldots, x)\) into the orthogonal summands of the target in set \(j\), which are counted from 1 in the order of the basis.
{"matrix": [
[1, 0],
[0, 1],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{1, 2\}\)
A morphism \(U(2) \to U^{3} \oplus \langle -4 \rangle\): \(b_T(\varphi x, \varphi y) = 2 \, b_S(x, y)\).
Summand \(j\) of the source maps by \(x \mapsto (x, \ldots, x)\) into the orthogonal summands of the target in set \(j\), which are counted from 1 in the order of the basis.
{"matrix": [
[1, 0],
[0, 1],
[1, 0],
[0, 1],
[0, 0],
[0, 0],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}
Diagonal into the summands \(\{1, 2, 3\}\)
A morphism \(U(3) \to U^{3} \oplus \langle -4 \rangle\): \(b_T(\varphi x, \varphi y) = 3 \, b_S(x, y)\).
Summand \(j\) of the source maps by \(x \mapsto (x, \ldots, x)\) into the orthogonal summands of the target in set \(j\), which are counted from 1 in the order of the basis.
{"matrix": [
[1, 0],
[0, 1],
[1, 0],
[0, 1],
[1, 0],
[0, 1],
[0, 0]
],
"row_subdivisions": [],
"column_subdivisions": []}