This process is very helpful for solving linear equations, computing determinants, and finding inverses.įor example, let's take a 2x2 matrix $$$A $$$: $$A=\left $$ $$$U $$$ is an upper triangular matrix (all entries below the main diagonal are zero).$$$L $$$ is a lower triangular matrix (all entries above the main diagonal are zero). LU decomposition, sometimes referred to as LU factorization, is a strategy in linear algebra that decomposes a matrix into the product of a lower triangular matrix $$$L $$$ and an upper triangular matrix $$$U $$$.įormally, if $$$A $$$ is a matrix, we can write this as: $$A=LU, $$ However, not all matrices can be decomposed in all ways (this depends on their characteristics). Common types include LU, eigenvalue, and singular value decompositions. These simpler matrices, often having specific properties, are easier to use for computations such as solving linear equations, finding determinants, or calculating inverses. Matrix decomposition, also known as matrix factorization, is the process of breaking down a given matrix into a product of simpler matrices. You can then use these matrices for further computations or analysis as per your requirements. The $$$L $$$ and $$$U $$$ matrices will be displayed as the output of the calculator. It will also output a permutation matrix $$$P $$$ if it is different from the identity matrix. The LU solver will then process your input and quickly decompose your matrix into a lower triangular matrix $$$L $$$ and an upper triangular matrix $$$U $$$. Input the elements of the matrix you wish to decompose into the provided fields.Ĭlick on the "Calculate" button. How to Use the LU Decomposition Calculator? Our LU solver will help you to decompose your matrix quickly and easily. The LU Decomposition Calculator is an online tool for immediate matrix factorization.
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