By applying the singular value decomposition of matrix and the properties of Frobenius matrix norm, we have obtained the range of the rank and the least-squares solution expression of under rank .... Definition: The LU Decomposition of a Matrix Consider a matrix 𝐴. Then, the "LU decomposition" requires finding a lower-triangular matrix L and an upper-triangular matrix U such that L U = 𝐴. This is sometimes referred to as the "LU factorization" of a matrix. We will demonstrate this with the simplest possible example of a 2 × 2 matrix. A sintering–CO2 decomposition process for preparation of pseudo-boehmite is proposed for clean valorization of high-alumina fly ash. The effects of different synthesis conditions on the crystal structure and textual properties of the pseudo-boehmite were studied systematically. The results showed that the main product was NaAlCO3(OH)2 when the. "/>Properties of lu decomposition