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Added on 06/23/07
Let be an matrix with entries in . A generalized inverse, denoted by , is an matrix with entries in , such that Examples * Let Then any matrix of the form where and , is a generalized inverse. * Using the same example from above, if , then we have an...
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Let be an matrix with entries in . A generalized inverse, denoted by , is an matrix with entries in , such that Examples * Let Then any matrix of the form where and , is a generalized inverse. * Using the same example from above, if , then we have an example of the Moore-Penrose generalized inverse, which is a unique matrix. * Again, using the example from above, if and is any complex number, we have an example of a Drazin inverse. Remark Generalized inverse of a matrix has found many applications in statistics. For example, in general linear model, one solves the set of normal equations to get the MLE of the parameter vector . If the design matrix is not of full rank (this occurs often when the model is either an ANOVA or ANCOVA type) and hence is singular. Then the MLE can be given by See less 
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