Flashcards
4.2.8 Vectors
Cards in this deck (14)
- 1VectorsVectors are mathematical constructs consisting of a magnitude and distance.
In computer science they are type of 1 dimensional data structure, like an array or a linked list.
Unlike an array, new values can be added to a vector and its size can be increased or decreased as needed - 2RepresentationA vector is an abstract data type, like a graph or tree, and needs to be represented using other types.
Like a graph can be represented with an adjacency matrix or list, a vector can be represented with an array or function
We visually represent it as an arrow, with a given size and direction. - 3VectorsVectors are mathematical constructs consisting of a magnitude and distance.
In computer science they are type of 1 dimensional data structure, like an array or a linked list.
Unlike an array, new values can be added to a vector and its size can be increased or decreased as needed - 4RepresentationA vector is an abstract data type, like a graph or tree, and needs to be represented using other types.
Like a graph can be represented with an adjacency matrix or list, a vector can be represented with an array or function
We visually represent it as an arrow, with a given size and direction. - 5RepresentationVector, v, could be shown as follows:
This could be represented by taking the x and y distances.
?=(8¦3) - 63D vectorBy adding a z axis, we can get a 3-dimensional vector
While our perception of the universe stops here, maths works just fine for 4, 5 or 6 dimensional vectors.
In computing, where use of vectors is not always tied to the direction and magnitude idea, vectors with multiple values are common.
Because of this, they are usually represented like arrays:
v= (1,3,6) or v=[1,3,5] - 7Representation4-Vector over ℝ (Written as ℝ4)
This means a vector of 4 elements, each of which are Real Numbers
This could be represented as an array in Java:
float[] myVector = new float[4] - 8RepresentationA vector can also be represented by a function.
The function can be represented with the notation F:XB
Where F is the function
X is the domain (all possible inputs)
B is the co-domain (all possible outputs) - 9Dot ProductDot product combines two vectors to create a single number
A=(a1,a2)
B=(b1,b2)
A.B = a1×b1 + a2×b2 - 10Use of dot productParity Bit
Performing dot product on a vector of 0s and 1s with a vector of 1s will result in the parity bit:
[1,1,1,1].[1,0,1,1] = 1
[1,1,1,1].[0,1,0,1] = 0
Angle between vectors
The dot product is the cosine of the angle between vectors, multiplied by their lengths - 11Convex CombinationCombination is where a third vector is created by combining two others.
We don’t need to know any specific methods to do this (such as cross-product).
Several combination techniques exist that create a third vector within the vector space of the originals. This is called convex combination - 12Convex Combination example
- 13Uses of vectorsVectors are used heavily in graphics.
Vector graphics store the information about shapes as vectors
How could this shape be stored as vectors? - 14—
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- Flashcards on 4.2.8 Vectors, created by Ed Allen on 05/05/2020.
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