matrix an orthogonal matrix a diagonal matrix and an upper triangular matrix the matrices p d r have the size 2 u00d7 2 the matrix q has the size 4 u00d7 2 the lr unit 207 decreases for the second column of the r 1 greater than one in absolute value off diagonal elements of the matrix r 1 and then the previous columns of the r 1 multiplied by corresponding integers are subtracted from the current column for example if the absolute value of one of components r jk real or imaginary is greater than 1 the real and imaginary parts of the r jk are rounded off thus obtaining a complex integer quantity u03bc and the column j is u03bc times subtracted from the column k i e each element of the column j is multiplied by the integer complex u03bc and subtracted from the corresponding element of the column k in so doing the off diagonal elements of columns of the matrix r 1 are processed sequentially upward from the diagonal simultaneously with altering decreasing of the off diagonal elements the matrix r 1 the transforming matrix t such that r 1 t u2212 1 remains unchanged the subtraction of the column having the index j from the column k results in the following transformation of the matrices r 1 and t r 1new m k r 1 m k u2212 u03bc r 1 m j t 1new m k t 1 m k u2212 u03bc t 1 m j equation 5 where m refers.