Chapter 5: Matrix Approaches to Simple Linear Regression
Chapter 5: Matrix Approaches to Simple Linear Regression
Chapter 5: Matrix Approaches to Simple Linear Regression
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<strong>Linear</strong> DependenciesOverview<strong>Matrix</strong> AlgebraAlgebraMore Matrices➤ <strong>Linear</strong>Dependencies➤ Rank of a <strong>Matrix</strong>➤ Some BasicResults forMatricesGeneral <strong>Linear</strong>ModelOther <strong>Matrix</strong>ProductsWrapping Up● A set of vec<strong>to</strong>rs are said <strong>to</strong> be linearly dependent ifa 1 , a 2 , . . .,a k exist, and:✦ a 1 x 1 + a 2 x 2 + . . . + a k x k = 0.✦ a 1 , a 2 , . . .,a k are not all zero.● Such linear dependencies occur when a linear combinationis added <strong>to</strong> the vec<strong>to</strong>r set.● Matrices comprised of a set of linearly dependent vec<strong>to</strong>rs aresingular.● A set of linearly independent vec<strong>to</strong>rs forms what is called abasis for the vec<strong>to</strong>r space.● Any vec<strong>to</strong>r in the vec<strong>to</strong>r space can then be expressed as alinear combination of the basis vec<strong>to</strong>rs.Lecture 17 Psychology 790
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