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Reference.org
Bidiagonal matrix
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a bidiagonal matrix is a <a href="/facts/Banded_matrix/Iz803N35">banded matrix</a> with non-zero entries along the main diagonal and <i>either</i> the diagonal above or the diagonal below. This means there are exactly two non-zero diagonals in the matrix. </p><p>When the diagonal above the main diagonal has the non-zero entries the matrix is upper bidiagonal. When the diagonal below the main diagonal has the non-zero entries the matrix is lower bidiagonal. </p><p>For example, the following matrix is upper bidiagonal: </p> ( 1 4 0 0 0 4 1 0 0 0 3 4 0 0 0 3 ) {\displaystyle {\begin{pmatrix}1&4&0&0\\0&4&1&0\\0&0&3&4\\0&0&0&3\\\end{pmatrix}}} <p>and the following matrix is lower bidiagonal: </p> ( 1 0 0 0 2 4 0 0 0 3 3 0 0 0 4 3 ) . {\displaystyle {\begin{pmatrix}1&0&0&0\\2&4&0&0\\0&3&3&0\\0&0&4&3\\\end{pmatrix}}.}