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Flashcards in LinAlg Deck (50):
1

linear equation

1

2

linear system

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3

possible number of solutions

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4

matrix

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5

size of a matrix

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6

entries

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7

diagonal entry

7

8

lower/upper triangular

8

9

matrix operations

9
addition/subtraction, scalar multiple, transposition, product, power

10

idempotent

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11

identity matrix

11

12

inverse

12

13

Gaussian elimination

13
defn, algorithm

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solving Ax=b

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15

inverse of 2x2 matrix

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16

vector space

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defn, 10 axioms

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nullspace

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18

linear combination of vectors v_i

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19

span

19

20

linearly independent

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21

basis

21

22

dimension of V

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23

rank

23

24

metric

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4 properties

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inner product

25
5 properties

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norm

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4 properties

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column/row space of A

27

28

transposition

28

29

permutation of n

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30

S_n

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31

determinant of 2x2 matrix

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32

properties of determinant function

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8 of em

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Laplace expansion

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34

adjugate matrix

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35

inverse matrix theorem

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Cramer's rule

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linear transformation

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defn, linear operator

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matrix representation of T

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39

kernel of T

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40

nullity of T

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range

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42

rank plus nullity theorem

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thrm, 4 equivalents

43

eigenvalue and corresponding eigenvector

43
defn, 3 facts

44

characteristic equation

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45

trace

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46

sum of eigenvalues

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product of eigenvalues

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48

eigenspace

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49

Cayley-Hamilton theorem

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50

diagonalizable

50
defn, 2 facts