LinAlg Flashcards
linear equation
1
linear system
2
possible number of solutions
3
matrix
4
size of a matrix
5
entries
6
diagonal entry
7
lower/upper triangular
8
matrix operations
9
addition/subtraction, scalar multiple, transposition, product, power
idempotent
10
identity matrix
11
inverse
12
Gaussian elimination
13
defn, algorithm
solving Ax=b
14
inverse of 2x2 matrix
15
vector space
16
defn, 10 axioms
nullspace
17
linear combination of vectors v_i
18
span
19
linearly independent
20
basis
21
dimension of V
22
rank
23
metric
24
4 properties
inner product
25
5 properties
norm
26
4 properties
column/row space of A
27
transposition
28
permutation of n
29
S_n
30
determinant of 2x2 matrix
31
properties of determinant function
32
8 of em
Laplace expansion
33
adjugate matrix
34
inverse matrix theorem
35
Cramer’s rule
36
linear transformation
37
defn, linear operator
matrix representation of T
38
kernel of T
39
nullity of T
40
range
41
rank plus nullity theorem
42
thrm, 4 equivalents
eigenvalue and corresponding eigenvector
43
defn, 3 facts
characteristic equation
44
trace
45
sum of eigenvalues
46
product of eigenvalues
47
eigenspace
48
Cayley-Hamilton theorem
49
diagonalizable
50
defn, 2 facts
