ReplaceAntidiagonal
Returns a matrix with its antidiagonal replaced by a given vector.
Syntax
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ReplaceAntidiagonal(A, v)-
Ais a matrix -
vis a vector
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Description
If A is an n×n matrix and v a vector of dimension n, then ReplaceAntidiagonal(A, v) returns the matrix obtained from A by replacing its antidiagonal with the components of v (in order, from the top-right to the bottom-left corner of A).
Examples
A ≔ ❨❨5, 1, 2, 3, 4❩, ❨4, 0, 2, 1, 7❩, ❨6, 3, 0, 4, 7❩, ❨4, 5, 2, 3, 9❩, ❨4, 0, 1, 2, 5❩❩
⎛5 1 2 3 4⎞ ⎜4 0 2 1 7⎟ ⎜6 3 0 4 7⎟ ⎜4 5 2 3 9⎟ ⎝4 0 1 2 5⎠
ReplaceAntidiagonal(A, ❨0, 0, 0, 0, i❩)
⎛5 1 2 3 0⎞ ⎜4 0 2 0 7⎟ ⎜6 3 0 4 7⎟ ⎜4 0 2 3 9⎟ ⎝i 0 1 2 5⎠