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