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365 Data Science - Mathematics > Introduction to Linear Algebra > Flashcards

Introduction to Linear Algebra Flashcards

1
Q

What is a matrix?

A

A matrix is a collection of numbers ordered in rows and columns

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2
Q

What is each of the values of a matrix calle?

A

an element

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3
Q

In Linear Algebra what are the two dimensions of the matrix?

A

Rows and Columns

Example matrix A with 2 rows and 3 columns. We say its dimensions are 2x3
Or
A is a 2 by 3 matrix

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4
Q

What is the last element in a matrix?

A

a mn

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5
Q

How do you calculate the total number of elements

A

m*n

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6
Q

A matrix can contain:

Numbers

Symbols

Expressions

All of the above

A

All of the above

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7
Q

How many elements does a matrix with dimensions m = 5 and n = 12 have?

5

12

60

120

A

60

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8
Q

What is a vector?

A

A vector is practically the simplest linear algebraic object

They sit somewhere between scalar and matrix as they have 1 dimension

ie. a 3 by 1 matrix

a matrix can be viewed a collection of vectors

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9
Q

What is a scalar?

A

A matrix with 1 row and 1 column

0 dimensions

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10
Q

What are the two types of vectors?

A

Row Vectors
Column Vectors

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11
Q

What is the length of a vector?

A

The number of elements in a vector

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12
Q

Choose the correct option. All numbers known from algebra are referred to as _________ in linear algebra.

Scalars

Vectors

Matrices

Tensors

A

Scalars

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13
Q

If a vector has a length of 3, it has:

3 rows

3 columns

3 rows and 3 columns

3 rows or 3 columns

A

3 rows or 3 columns

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14
Q

How many dimensions does a vector have?

0

1

2

3

A

1

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15
Q

If a scalar has 0 dimensions, what else has zero dimensions?

A

geometrical idea of a point
- no direction or size

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16
Q

In terms of geometry a scalar can be represented as:

a line

a square

a point

it cannot be represented geometrically

A

a point

17
Q

Geometrically a vector can be represented as:

A point

A line

A plane

A

A line

18
Q

A point

A line

A plane

A

A plane

19
Q

in python, what kind of vector is default?

A

a row vector

ie. an array

20
Q

What are tensors?

A

Tensors are a generalization of the concepts we have seen so far:

name - tensor rank
scalar = rank 0
vector = rank 1
matrix = rank 2
a collection of matrices = rank 3

21
Q

What is a Rank 3 tensor?

A

A collection of matrices
Dimensions of k x m x n

22
Q

Choose the best answer:

Scalars are type of tensors

Tensors are types of matrices

Matrices are types of vectors

it cannot be represented geometrically

A

Scalars are type of tensors

23
Q

A vector is a tensor by definition. Of what rank?

0

1

2

3

Other

A

Rank1

24
Q

What happens when we transpose the same vector twice?

A

It yields the same vector

25
Q

What does it mean to transpose a vector?

A

To change it from a linear to horizontal or vice versa
rows to columns and vice versa

ie. 1x3 to 3x1

26
Q

What is the difference between a dot product and tensor product?

A
27
Q

What is another name for the dot product?

A

inner or scalar product

because we multiplied two vectors and got a scalar

ie. multiply two arrays and get an int

The sum of the products of the corresponding elements

28
Q

What is the notation of the dot product?

A

a dot - “.” - signifying it is the dot product

29
Q

What happens when we multiply a scalar by a vector?

A

we get a vector with the same length

30
Q

What is the outcome of the dot product of the following two matrices?

A. B =
2x3 3x6

A

A. B C
2x3 3x6 = 2x6

31
Q

T or F - we always multiply a row vector by a column vector

A

T

32
Q

What are practical applications of linear algebra in data science?

A

vectorizing code
- input matrix - weights matrix(coefficients) - output matrix

imagine recognition
dimensionality reduction

33
Q

What is is called when we use linear algebra to compute many values simultaneously?

A

Array programming or vectorizing code

365 Data Science - Mathematics (1 decks)

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