線性代數的一些定理
Linear Algebra
Matrices
Basic Conceps
Theorem1. If matrices A, B, and C all have the same order,then
(a) the commutative law of addition holds; that is,
A + B = B + A
(b) Tne associatiove law of addition holds; that is,
A + (B + C) = (A + B) + C
Theorem2. If A and B are matrices of the same order and if a and b
denoted scalars, then the following distributive laws hold:
(a) a(A + B) = aA + aB
(b) (a + b)A = aA + bA
(c) (ab)A = a(bA)
Matrix Multiolication
Theorem If A, B and C have appropriate orders so that the
following additions and multiplications are defined, then
(a) A(BC) = (AB)C (associate law of multiplication)
(b) A(B + C) = AB + AC (left distributive law)
(c) (B + C)A = BA + CA (right distributive law)
Determinants
Properties of Determinants
Eigenvectors and Eigenvalues
Properties of Eigenvextors and Eigenvalues