Exam prep

Question 1

Reflexive relation

Answer 1

A is reflexive if there is an existence of (a,a). (A->A)

Question 2

Symmetric relation

Answer 2

A and B are symmetric if aRb and bRa. (A->B) and (B->A)

Question 3

Transistive relation

Answer 3

A, B and C is transitive if there exists a relation aRb, bRc and aRc.

Question 4

Linear equations - Consistent systems

Answer 4

Consistent if there is a solution which satisfies all of the equations. Minimum of one solution.

Question 5

Linear equations - Inconsistent system

Answer 5

Not consistent if there is not a solution that satisfies all the equations in the system.

Question 6

Linear (in)dependence

Answer 6

A vector is said to be linearly dependent if it can be defined as the combination of two other vectors in the set. If not, it is linearly independent. If a vector is adding another dimension to the span, it is linearly independent.

Question 7

Inverse matrix

Answer 7

The inverse of A is A^-1 only when: AA^(-1)=A^(-1)A=I.

Multiplying a linear transformation by its inverse corresponds to “playing” the transformation backwards.

Question 8

Determinant

Answer 8

The scale factor for the area (2D) or volume (3D) represented by the column vectors in a square matrix.

Question 9

Span

Answer 9

Set of all linear combinations of vectors. We ask what are all the possible vectors we can reach using only vector addition and scalar multiplication.

Question 10

Basis

Answer 10

Set of vectors with the characteristics that all other vectors in the space can be expressed as a linear combination of the vectors in the basis.

Set of linearly independent vectors that span the full space.

Question 11

Null space

Answer 11

The null space of a matrix A consists of all the vectors x such that Ax = 0 and x is not zero.

Solution to Ax = 0.

Question 12

Matrix dimension

Answer 12

Number of vectors in the basis. The basis needs to be linearly independent.

Question 13

Rank

Answer 13

The rank of a matrix is the number of nonzero rows in any matrix that is in row echelon form.

The number of linearly independent rows or columns of the matrix.

Question 14

Column space (range, image)

Answer 14

The columns space of matrix A is the span of its column vectors. Subspace of Rm.

Question 15

Row space

Answer 15

The row space of matrix A is the span of its row vectors. Subspace of Rn.

Question 16

Eigenvectors

Answer 16

The eigenvector for a linear transformation is an element of the vector space that will not change direction after it is transformed.

Question 17

Eigenvalue

Answer 17

An expression for how much the eigenvector is stretched by the linear transformation.

Question 18

Algorithmic complexity

Answer 18

The processing power usage of a computer to solve certain tasks decided by its underlying algorithm. Used to evaluate the algorithm, scalability and input size.

Question 19

Big O-notation

Answer 19

Given an expression for the number of operations needed to compute an algorithm, we want to know the asymptotic behaviour as size of the problem gets large.

Question 20

Higher order functions

Answer 20

A function that returns another function, or a function that accepts a function as an argument.

Question 21

Black box

Answer 21

Testing is done without the knowledge of the internal structure of the program. External or end-user perspective.

Question 22

White box

Answer 22

Testing is done with knowledge of the internal structure of the program. Main goal is to test the internal operation of the system. Focus on code structure.

Question 23

Raise exception

Answer 23

Typically used when you have detected an error condition, or some condition does not satisfy.

Question 24

Assertion

Answer 24

Similar to raise, but the exception is only raised if a condition is met. If the condition returns false, we get an AssertionError. Used for things that will run, but should not run for your program.

Question 25

Global variable

Answer 25

Variable declared outside of the function. Can be accessed inside or outside of a function.

Question 26

Local variable

Answer 26

Variable declared inside the function body.

Question 27

Enclosed variable

Answer 27

Variable that isn’t global or local. Seen in higher order functions.

Question 28

Built-in

Answer 28

All the names that are loaded into python. For example print().

Question 29

Relations

Answer 29

A relationship between sets of values.