Matrix rules for Econometrics Flashcards

1
Q

When are two matrices conformable in addition/subtraction?

A

When they both have the same number of rows (m) and columns (n)

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2
Q

What are the two main properties of Matrix addition/subtraction?

A

Commutative and Associative

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3
Q

What does Commutative in addition mean?

A

The order of the matrices is irrelevant:
A + B = B + A

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4
Q

What does Associative in addition mean?

A

The order in which matrices are added together does not matter:
A + (B + C) = (A + B) + C

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5
Q

When is the multiplication of two matrices conformable?

A

When the number of columns for the first matrix equals the number of rows of the second matrix:
(A: m x n)(B: n x p) = (C: m x p)

Where C = AB is the matrix product

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6
Q

Steps of Matrix multiplication

A
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7
Q

Why is it possible that when multiplying two matrices:
AB ≠ BA

A

Matrix multiplication is not commutative which means that that the order in which two matrices are multiplied matters. The case where AB = BA is only possible when matrices A and B have equal numbers of rows and columns

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8
Q

What is the reversal rule in matrix transposition?

A

Let C = AB. Matrix transposition flips the order of the product:
C’ = B’A’ which can be expressed as C = (AB)’

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9
Q

What is the result of a matrix being multiplied by the identity matrix?
For example: A x I

A

The original matrix - A
Hence, AI = IA = A

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10
Q

Steps for matrix inversion

A
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11
Q

What is AA^-1

A

The identity matrix I

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12
Q

What is the determinant of a matrix

A
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13
Q

When are two vectors orthogonal?

A

x’y = 0

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14
Q

Show that the inverse of an orthogonal matrix is its transpose:
A’ = A^-1

A
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15
Q

Importance of linear dependence and rank

A
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16
Q
A