This paper describes the mathematical structure of the Principal Component Analysis (PCA) and an application in the metal-mechanical sector in Colombia. The analytical and numerical procedure used, is detailed to find the principal components. It emphasizes in the square matrix QR algorithm procedure for calculating its own values `` and vectors which reduce the variables to be analyzed. The Principal Component Analysis is a statistical approach that simplifies the subjectivity of business decision makers, through the implementation of linear algebra and numerical analysis in reducing variables to analyze financial studies. The financial behavior of companies in the metalmechanical sector 2009-2010 can be explained by the operating profit, noncurrent liabilities and non-operating income.