LinAlg Flashcards

1
Q

linear equation

A

1

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2
Q

linear system

A

2

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3
Q

possible number of solutions

A

3

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4
Q

matrix

A

4

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5
Q

size of a matrix

A

5

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6
Q

entries

A

6

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7
Q

diagonal entry

A

7

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8
Q

lower/upper triangular

A

8

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9
Q

matrix operations

A

9

addition/subtraction, scalar multiple, transposition, product, power

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10
Q

idempotent

A

10

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11
Q

identity matrix

A

11

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12
Q

inverse

A

12

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13
Q

Gaussian elimination

A

13

defn, algorithm

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14
Q

solving Ax=b

A

14

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15
Q

inverse of 2x2 matrix

A

15

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16
Q

vector space

A

16

defn, 10 axioms

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17
Q

nullspace

A

17

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18
Q

linear combination of vectors v_i

A

18

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19
Q

span

A

19

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20
Q

linearly independent

A

20

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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
Q

inner product

A

25

5 properties

26
Q

norm

A

26

4 properties

27
Q

column/row space of A

A

27

28
Q

transposition

A

28

29
Q

permutation of n

A

29

30
Q

S_n

A

30

31
Q

determinant of 2x2 matrix

A

31

32
Q

properties of determinant function

A

32

8 of em

33
Q

Laplace expansion

A

33

34
Q

adjugate matrix

A

34

35
Q

inverse matrix theorem

A

35

36
Q

Cramer’s rule

A

36

37
Q

linear transformation

A

37

defn, linear operator

38
Q

matrix representation of T

A

38

39
Q

kernel of T

A

39

40
Q

nullity of T

A

40

41
Q

range

A

41

42
Q

rank plus nullity theorem

A

42

thrm, 4 equivalents

43
Q

eigenvalue and corresponding eigenvector

A

43

defn, 3 facts

44
Q

characteristic equation

A

44

45
Q

trace

A

45

46
Q

sum of eigenvalues

A

46

47
Q

product of eigenvalues

A

47

48
Q

eigenspace

A

48

49
Q

Cayley-Hamilton theorem

A

49

50
Q

diagonalizable

A

50

defn, 2 facts