INDUMAT Definitions (Quiz 2) Flashcards
Rectangular array of numbers
Matrix
Ordered list of n numbers
Vector
Matrix where the number of rows equals the number of columns (m = n)
Square Matrix
m
Number of Rows
n
Number of Columns
Square matrix for which every term off the main diagonal is zero
Diagonal Matrix
Diagonal matrix for which all elements of the main diagonal are equal
Scalar Matrix
Scalar Matrix for which all elements of the main diagonal are 1
Identity Matrix
A matrix where elements below the main diagonal are all zeroes
Upper Triangular Matrix (Right Triangular Matrix)
A matrix where the elements above the main diagonal are all zeroes
Lower Triangular Matrix (Left Triangular Matrix)
Matrix where all elements are zeroes
Null Matrix
i
Row
j
Column
Matrix with only one row
Row Vector
Matrix with only one column
Column Vector
True or False. A matrix is symmetrical if A = A^T.
True
A matrix is considered to be in Reduced Row Echelon Form when:
- The first non-zero entry in any row is the number 1, called pivots. (So each row can have zero or one pivot).
- A pivot is the only non-zero entry in its column (so each column can have zero or one pivot)
- Rows are ordered such that rows of all zeros are at the bottom and the pivots are in column order.
Type of matrix that has a determinant value of zero and does not have an inverse.
Singular Matrix
Type of matrix that has a determinant value and has an inverse.
Non-Singular Matrix (Standard Matrix)
True or False. Identity matrices are nonsingular.
True
In iteration methods, if the error is decreasing, then _________.
It is converging towards an answer.
If a matrix undergoing an iterative method is not diagonally dominant, then _________.
You must interchange the rows such that the diagonal consists of the highest coefficients of the matrix.
In special cases, when no solution exists, we have an _________ System of Equations.
Inconsistent
In special cases, we have an _________ System of Equations if an infinite number of solutions exist.
Over-determined
A solution obtained when all (n-m) variables are required to 0 (ex. 0 0 16 12)
Basic Solution
A solution obtained when at least 1 of the (n-m) variables is not equated to 0 (ex. 1 1 8 6)
Non-Basic Solution
A solution where all values of the variables are non-negative (ex. 1 1 8 6)
Feasible Solution
A basic solution where all values
of the remaining m variables are non-negative
Feasible Basic Solution
A solution where at least 1 of the
variable assumes a negative value.
Non-feasible Solution
A solution where at least 1 of the
basic variable has a value of zero.
Degenerate Solution
If the determinant of a matrix is equal to zero, then the solution would either be ________ or __________,
No solution or Infinitely many solutions
In the Special Cases for iterative methods, m refers to ___________ while n refers to _________.
m = Number of equations
n = Number of unknowns
In special cases, no solution exists when ___________.
Determinant of the matrix is equal to 0
RDs does not equal to 0
Inverse of a 2x2 Matrix Formula
1/ad-bc x [d -b]
[-c a]
wherein it is the determinant times the adjoint of the matrix
In special cases, exactly one solution exists when _________.
Determinant of the matrix is not equal to 0
In special cases, infinitely many solutions exist when _________.
Determinant of the matrix is equal to 0
RDs equal to 0
Conditions for Convergence for Root Finding
- |g’(x)| ->1; convergence is slow
- |g’(x)| < 1; there will be convergence
- |g’(x)| > 1; no convergence (divergent)
