Matrix Algebra Flashcards

1
Q

diagonal matrix

A

if a matrix conatains zeros in all off-diagonal positions

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2
Q

identify matrix

A

a diagonal matrix with a 1 in each diagonal position

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3
Q

upper triangular matrix

A

a square matrix with zeros below the diagonal

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4
Q

j

A

A vector 1

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5
Q

J

A

a square matrix of 1’s

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6
Q

o

A

a vector of zeros

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7
Q

O

A

a matrix of zeros

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8
Q

(A + B)’ =

A

A’ + B’

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9
Q

(A - B)’ =

A

A’ - B’

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10
Q

conformable

A

the number of colums in A must be the same as the number of rows in B

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11
Q

A (B + C) =

A

AB + AC

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12
Q

A (B - C) =

A

AB - AC

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13
Q

(A + B) C =

A

AC + BC

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14
Q

(A - B) C =

A

AC - BC

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15
Q

(A - B) (C - D)

A

(A - B)C - (A - B) D

= AC - BC - AD + BD

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16
Q

ABC =

A

A (BC) = (AB) C

17
Q

ABC + ADC =

A

A (B + D) C

18
Q

X’X - X’AX =

A

X’(X - AX) = X’ (1 - A )X

19
Q

a’a

A

dot product

20
Q

aa’

A

matrix product

21
Q

j’j =

A

n

22
Q

jj’ =

A

J

23
Q

a2’ =

A

(a21 a22 a23 a24)

24
Q

Partitioned Matrices

A

Partition a matrix into submatrices

25
Q

Linearly dependent

A

if constants c1, c2, …., cn (not all zero) can be found such that
c1a1 + c2a2 + … + can = 0

26
Q

If A is n times p, the maximum possible rank of A is the smaller of n and p

A

Full rank (full row rank or full column rank)

27
Q

A’

A

transpose by interchanging rows and columns