Proposition 7.3 If α : V → V is self-adjoint, then 1) Every eigenvalue
... If V is an inner product space, then any subspace W is also an inner product space with respect to the same inner product. Furthermore, if α : V → V is self-adjoint and W is α-invariant, then α|W is self-adjoint as well. Lemma 7.5 If α : V → V is self-adjoint and W is α-invariant, then W ⊥ = {v ∈ V ...
... If V is an inner product space, then any subspace W is also an inner product space with respect to the same inner product. Furthermore, if α : V → V is self-adjoint and W is α-invariant, then α|W is self-adjoint as well. Lemma 7.5 If α : V → V is self-adjoint and W is α-invariant, then W ⊥ = {v ∈ V ...
Notes
... Any symmetric positive definite matrix A can be written as A QQ where Q is some nonsingular matrix. For example, consider the covariance matrix 2V . This matrix is positive def. So its inverse also is. So we can decompose it V 1 QQ . We premultiply both sides of ...
... Any symmetric positive definite matrix A can be written as A QQ where Q is some nonsingular matrix. For example, consider the covariance matrix 2V . This matrix is positive def. So its inverse also is. So we can decompose it V 1 QQ . We premultiply both sides of ...
Math 200 Spring 2010 March 12 Definition. An n by n matrix E is
... 1. For each of the elementary matrices in the first examples above, find the inverse. Is the inverse an elementary matrix? If so, what is its defining elementary row operation? How does that relate to the defining row operation of the original matrix? 2. For each matrix A, find (i) a basis for ker(A ...
... 1. For each of the elementary matrices in the first examples above, find the inverse. Is the inverse an elementary matrix? If so, what is its defining elementary row operation? How does that relate to the defining row operation of the original matrix? 2. For each matrix A, find (i) a basis for ker(A ...
