Flashcards in Vectors & Matrices Deck (8)

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1

## What is a vector?

###
Sequence of nums but diff from sequence as position of each value is significant. Sequence comp creates sequence in same way as set comp, with constraint of 1 generating variable + its value taken in order from set of whole nums.

E.g. [x|x∈{1,…,3}]. ‘inds(S)’ means {1,…,len(S)}

2

## How do we add vectors?

### Add 2 vectors to create new one by adding corresponding elements. Must be of same kind. E.g. (2,3,1,200) + (2,3,1,300) = (4,6,2,500) so A + B = [A(i)+B(i)|i∈inds(A)]

3

## What is a scalar?

### Single number. To multiply vector by scalar, multiply each element by scalar. If s is scalar + v is vector, product of s and v is s*v = [s*v(i)|i∈ inds(s)]

4

## How do you multiply 2 vectors?

###
Can multiply 2 vectors + get scalar answer. If a and b are vectors of same length, a is horizontal + b is vertical, then scalar product of a and b is:

len (a)

a * b = ∑ a(i) * b(i)

i=1

5

## How do we multiply matrices?

###
(0.60 0.50)

(0.90 0.80)

Matrices e.g. (2,3,1,200) * = (6.79 8.10)

(0.80 0.70)

(0.01 0.02)

Matrix addition + multiplication are associative, matrix multiplication distributes over matrix addition.

6

## What is a matrix?

### Sequence of vectors where each vector is of same length. If M is matrix, then M(r) is rth row, within this row, M(r)(c) is cth element (column c). Row, then column. Can be represented in expression boxes as sequence of sequences. C = A*B means C will have A rows and B columns.

7

## Why do we use vectors of vectors?

### Number of multiplications + additions hasn’t been reduced by using vectors of vectors, benefit is keeping track of values.

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