Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A bidiagonal matrix is a matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below. So that means there are two non zero diagonal in the matrix. 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.

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