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MTM[diag] - extract the diagonals from a matrix or create a diagonal matrix
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Calling Sequence
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diag(A)
diag(A, k)
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Parameters
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A
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matrix, vector, array, or scalar
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k
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(optional) integer
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Description
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For a matrix A, the diag(A) command returns the main diagonal of A as a (column) vector.
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For a matrix A, the diag(A, k) command returns the (column) vector corresponding to the diagonal of A, specified by the selection parameter k.
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For a vector A, the diag(A) command returns a matrix with the entries of A along the main diagonal, and 0 everywhere else.
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For a vector A, the diag(A, k) command returns a matrix with the entries of A along the diagonal specified by the selection parameter k.
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The diagonals of a matrix are indexed using signed integers, where the main diagonal has index 0. Superdiagonals are indexed with positive integers and subdiagonals are indexed with negative integers.
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Examples
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![A := Matrix([[1, 2, 1], [4, 5, 6], [2, 8, 1]])](/support/helpjp/helpview.aspx?si=7594/file04789/math99.png)
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![A := Matrix([[1, 2, 1], [4, 5, 6], [2, 8, 1]])](/support/helpjp/helpview.aspx?si=7594/file04789/math102.png)
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](/support/helpjp/helpview.aspx?si=7594/file04789/math109.png)
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](/support/helpjp/helpview.aspx?si=7594/file04789/math116.png)
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](/support/helpjp/helpview.aspx?si=7594/file04789/math123.png)
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![B := Vector([4, 5, 6])](/support/helpjp/helpview.aspx?si=7594/file04789/math127.png)
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](/support/helpjp/helpview.aspx?si=7594/file04789/math130.png)
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![Matrix([[4, 0, 0], [0, 5, 0], [0, 0, 6]])](/support/helpjp/helpview.aspx?si=7594/file04789/math137.png)
| (6) |
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![Matrix([[0, 4, 0, 0], [0, 0, 5, 0], [0, 0, 0, 6], [0, 0, 0, 0]])](/support/helpjp/helpview.aspx?si=7594/file04789/math144.png)
| (7) |
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![Matrix([[0, 0, 0, 0], [4, 0, 0, 0], [0, 5, 0, 0], [0, 0, 6, 0]])](/support/helpjp/helpview.aspx?si=7594/file04789/math151.png)
| (8) |
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