Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here  develop methods for decomposing a matrix C into a product XY, where the factors X and Y are required to minimize their distance from an arbitrary pair \(X_0\) and \(Y_0\). This type of decomposition, a projection to a matrix product constraint, in combination with projections that impose structural properties on X and Y, forms the basis of a general method of decomposing a matrix into factors with specified properties. Results are presented for the application of these methods to a number of hard problems in exact factorization.
['Veit Elser']
I am writing a research paper on a idea Matrix product constraints by projection methods
[{"from": "human", "value": "I am writing a research paper on a idea Matrix product constraints by projection methods"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here  develop methods for decomposing a matrix C into a product XY, where the factors X and Y are required to minimize their distance from an arbitrary pair \\(X_0\\) and \\(Y_0\\). This type of decomposition, a projection to a matrix product constraint, in combination with projections that impose structural properties on X and Y, forms the basis of a general method of decomposing a matrix into factors with specified properties. Results are presented for the application of these methods to a number of hard problems in exact factorization."}]