Extensions to complex numbers
... Generalization: Normal matrix A complex matrix N is called normal, if NH N = N N H . • Normal matrices contain symmetric, skewsymmetric, orthogonal, Hermitian, skewHermitain and unitary as special cases. • We can find a unitary matrix U, such that N can be written as UDUH, for some diagonal matrix ...
... Generalization: Normal matrix A complex matrix N is called normal, if NH N = N N H . • Normal matrices contain symmetric, skewsymmetric, orthogonal, Hermitian, skewHermitain and unitary as special cases. • We can find a unitary matrix U, such that N can be written as UDUH, for some diagonal matrix ...
Representing the Simple Linear Regression Model as a Matrix
... ei2 eTe . In terms of the hat matrix this becomes SSE YT I H Y , where we have ...
... ei2 eTe . In terms of the hat matrix this becomes SSE YT I H Y , where we have ...
Practice Exam 2
... where, u1 + u2 ∈ H because H is a subspace, thus closed under addition; and v1 + v2 ∈ K similarly. This shows that w1 + w2 can be written as the sum of two vectors, one in H and the other in K. So, again by definition, w1 + w2 ∈ H + K, namely, H + K is closed under addition. For scalar multiplicatio ...
... where, u1 + u2 ∈ H because H is a subspace, thus closed under addition; and v1 + v2 ∈ K similarly. This shows that w1 + w2 can be written as the sum of two vectors, one in H and the other in K. So, again by definition, w1 + w2 ∈ H + K, namely, H + K is closed under addition. For scalar multiplicatio ...
Fast Monte-Carlo Algorithms for Matrix Multiplication
... Given a row of A – say A(i) – the algorithm computes a good fit for the row A(i) using the rows in R as the basis, by approximately solving ...
... Given a row of A – say A(i) – the algorithm computes a good fit for the row A(i) using the rows in R as the basis, by approximately solving ...
