Inverse Half-vectorization
This function returns the symmetric matrix constructed from a half-vectorization.
vech2full(x)
x |
an input single column or single row matrix. |
The half-vectorization of an input matrix consists of the elements in the lower triangle of the matrix, including the elements along the diagonal of the matrix, as a column vector. The column vector is created by traversing the matrix in column-major order. The inverse half-vectorization takes a vector and reconstructs a symmetric matrix such that vech2full(vech(x)) is identical to x if x is symmetric.
Note that very few vectors have the correct number of elements to construct a symmetric matrix. For example, vectors with 1, 3, 6, 10, and 15 elements can be used to make a symmetric matrix, but none of the other numbers between 1 and 15 can. An error is thrown if the number of elements in x cannot be used to make a symmetric matrix.
vech2full(1:10) matrix(1:16, 4, 4) vech(matrix(1:16, 4, 4)) vech2full(vech(matrix(1:16, 4, 4)))
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