Notes on Matrix Calculus
... (also combining these results means that Tm,n is an orthogonal matrix). The matrix operator Tm,n is a permutation matrix, i.e., it is composed of 0s and 1s, with a single 1 on each row and column. When premultiplying another matrix, it simply rearranges the ordering of rows of that matrix (postmult ...
... (also combining these results means that Tm,n is an orthogonal matrix). The matrix operator Tm,n is a permutation matrix, i.e., it is composed of 0s and 1s, with a single 1 on each row and column. When premultiplying another matrix, it simply rearranges the ordering of rows of that matrix (postmult ...
Vector Spaces and Linear Transformations
... If H is a subspace of V , then H is closed for the addition and scalar multiplication of V , i.e., for any u, v ∈ H and scalar c ∈ R, we have u + v ∈ H, cv ∈ H. For a nonempty set S of a vector space V , to verify whether S is a subspace of V , it is required to check (1) whether the addition and s ...
... If H is a subspace of V , then H is closed for the addition and scalar multiplication of V , i.e., for any u, v ∈ H and scalar c ∈ R, we have u + v ∈ H, cv ∈ H. For a nonempty set S of a vector space V , to verify whether S is a subspace of V , it is required to check (1) whether the addition and s ...
