Exam prep Flashcards
Reflexive relation
A is reflexive if there is an existence of (a,a). (A->A)
Symmetric relation
A and B are symmetric if aRb and bRa. (A->B) and (B->A)
Transistive relation
A, B and C is transitive if there exists a relation aRb, bRc and aRc.
Linear equations - Consistent systems
Consistent if there is a solution which satisfies all of the equations. Minimum of one solution.
Linear equations - Inconsistent system
Not consistent if there is not a solution that satisfies all the equations in the system.
Linear (in)dependence
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.
Inverse matrix
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.
Determinant
The scale factor for the area (2D) or volume (3D) represented by the column vectors in a square matrix.
Span
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.
Basis
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.
Null space
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.
Matrix dimension
Number of vectors in the basis. The basis needs to be linearly independent.
Rank
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.
Column space (range, image)
The columns space of matrix A is the span of its column vectors. Subspace of Rm.
Row space
The row space of matrix A is the span of its row vectors. Subspace of Rn.
Eigenvectors
The eigenvector for a linear transformation is an element of the vector space that will not change direction after it is transformed.
Eigenvalue
An expression for how much the eigenvector is stretched by the linear transformation.
Algorithmic complexity
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.
Big O-notation
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.
Higher order functions
A function that returns another function, or a function that accepts a function as an argument.
Black box
Testing is done without the knowledge of the internal structure of the program. External or end-user perspective.
White box
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.
Raise exception
Typically used when you have detected an error condition, or some condition does not satisfy.
Assertion
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.
Global variable
Variable declared outside of the function. Can be accessed inside or outside of a function.
Local variable
Variable declared inside the function body.
Enclosed variable
Variable that isn’t global or local. Seen in higher order functions.
Built-in
All the names that are loaded into python. For example print().
Relations
A relationship between sets of values.
