1.6 Matrices
... are working with is not a true binary operation as defined in Section 1.4. With a binary operation on a set A, it must always be possible to combine any two elements of A and obtain a unique result of the operation. Multiplication of matrices does not have this feature, since the product of two matr ...
... are working with is not a true binary operation as defined in Section 1.4. With a binary operation on a set A, it must always be possible to combine any two elements of A and obtain a unique result of the operation. Multiplication of matrices does not have this feature, since the product of two matr ...
Projection Operators and the least Squares Method
... Proof of the Theorem. We can prove this as follows. Let {a1 , a2 , · · · ar } be a basis for S. Now let A := (a1 , a2 , · · · ar ). This is an n × r matrix and its null space N (A) = {0} since the columns are linearly independent. The square matrix AT A is nonsingular. To see that it suffices to show ...
... Proof of the Theorem. We can prove this as follows. Let {a1 , a2 , · · · ar } be a basis for S. Now let A := (a1 , a2 , · · · ar ). This is an n × r matrix and its null space N (A) = {0} since the columns are linearly independent. The square matrix AT A is nonsingular. To see that it suffices to show ...
