Linear Algebra Terminology Flashcards
(36 cards)
How do you say:
R or R^1
The real number line
How do you say:
R^n
The n-dimensional vector space
or
The set of ordered n-tuples of real numbers.
How do you say:
R^+
The nonnegative reals
How do you say:
Z
The set of integers
How do you say:
Z^+
The set of nonnegative integers
How do you say:
Z^n
The set of ordered n-tuples of integers
How do you say:
S = {a, b, c, d}
S is a set of elements a, b, c, d.
How do you say:
S = {x: P(x)}
S is the set defined to contain all elements x for which a condition P is true.
How do you say:
|S|
The size of set S
How do you say:
f: S –> T
A mapping f from set S to set T
How do you say:
2^s
The set of all subsets of S
How do you say:
A = [a_ij]
Matrix A (with dimensions mxn) With element a_ij in Row i and Column j.
How do you say:
a_i
The n-vector consisting of the ith row of A
How do you say:
A_j
The m-vector which is the jth column of A
All vectors x are…
Column vectors
All vectors x’ are…
Row vectors
How do you say:
det (A)
The determinant of A (which must be a square matrix)
What is a multigraph?
Graphs with repeated edges. (Two vertices share more than one edge.)
What is a directed graph? Or a digraph?
A graph with directions assigned to its edges.
D = (V, A)
V is the vertices
A is the arcs, ordered pairs of vertices.
What is the degree of a vertex?
The number of edges incident upon that vertex.
Aka, number of edges it has
What is a walk?
A sequence of vertices/nodes, 1, 2, 3, 4
Where 1 has an edge to 2,
2 has an edge to 3,
3 has an edge to 4
What is a path?
A closed walk, where the first vertex connects to the last vertex of the walk.
What is a circuit or cycle?
A path with no repeated vertices
How do you calculate the length of a path?
If it goes from v_1 to v_k, it’s k-1
