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Block matrices can be constructed either by listing the blocks, or by
joining together smaller matrices horizontally, vertically or diagonally.
The matrix constructed from the given block matrices, which should all have the
same dimensions, and should be given as a sequence of m.n block
matrices (given in row major order, in other words listed across rows).
BlockMatrix(rows) : [ [ Mtrx ] ] -> Mtrx
The matrix constructed from the given block matrices, which should all
have the same dimensions, and should be given as a sequence of m rows,
each containing n block matrices.
Given a matrix X with r rows and c columns, and a matrix Y
with r rows and d columns, both over the same coefficient ring R,
return the matrix over R with r rows and
(c + d) columns obtained by joining X and Y horizontally (placing
Y to the right of X).
HorizontalJoin(T) : < Mtrx > -> Mtrx
Given a sequence Q or tuple T of matrices, each having the same number of rows and
being over the same coefficient ring R,
return the matrix over R
obtained by joining the elements of Q or T horizontally in order.
Given a matrix X with r rows and c columns, and a matrix Y
with s rows and c columns, both over the same coefficient ring R,
return the matrix with (r + s) rows and c columns over R obtained
by joining X and Y vertically (placing Y underneath X).
VerticalJoin(T) : < Mtrx > -> Mtrx
Given a sequence Q or tuple T of matrices, each having the same number
of columns and being over the same coefficient ring R,
return the matrix over R
obtained by joining the elements of Q or T vertically in order.
Given matrices X with a rows and b columns and Y with c rows
and d columns, both over the same coefficient ring R, return the
matrix with (a + c) rows and (b + d) columns over R obtained by
joining X and Y diagonally (placing Y diagonally to the right of
and underneath X, with zero blocks above and below the diagonal).
DiagonalJoin(T) : < Mtrx > -> Mtrx
Given a sequence Q or tuple T of matrices, each being over the same
coefficient ring R, return the matrix over R obtained by joining
the elements of Q or T diagonally in order.
Given an m x n matrix A and a p x q matrix B, both
over a ring R, return the Kronecker product of A and B, which
is the mp x nq matrix C over R such that
the ((i - 1)p + r, (j - 1)q + s)-th entry of C is the
(i, j)-th entry of A times the (r, s)-th entry of B,
for 1≤i≤m, 1≤j≤n, 1≤r≤p and 1≤s≤q.
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