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Matrix Test
Matrix Yo
41
Mathematics
Undergraduate 4
02/14/2012

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Term
linear equation
Definition
An equation that can be written in the form a1x1 + a2x2 + ... + anxn = b. where b and the coefficients a1....an are real or complex numbers
Term
solution set
Definition
The set of all linear combinations of v.....vp. Also the subspace spanned (or generated) b v1......vp
Term
consistent
Definition
a linear system with at least one solution
Term
inconsistent
Definition
a linear system with no solution
Term
coefficient matrix
Definition
a matrix whose entries are the coefficients of a system of linear equations
Term
augmented matrix
Definition
A marix made up of a coefficient matrix for a lineaer system and one or more columns to the right. Each extra column contains the constants from the right side of a system with the given coefficient matrix.
Term
row operation (three permitted types)
Definition
switch the rows
addition subtraction
multiplications
Term
row equivalent
Definition
two matrices for which there exists a finite sequence of row operrations that transforms one matrix into another
Term
row echelon form
Definition
Term
reduced row echelon form
Definition
A reduced echelon matrix that is row equivalent to a given matrix
Term
leading entry
Definition
the leftmost nonzero entry in a row of a matrix
Term
pivot position
Definition
a position in a matrix A that corresponds to a leading entry in an echelon form of A
Term
pivot column
Definition
A column that contains a pivot position
Term
free variable
Definition
any variable in a linear system that is not a basic variable
Term
parameter
Definition
see book
Term
parametric solution
Definition
see book
Term
vector
Definition
a list of numbers; a matrix with only one column. In general any element of a vector space.
Term
column vector
Definition
A matrix with only one column, or a single column of a matrix that has several columns
Term
row vector
Definition
A matrix with only one row, or a single row of a matrix that has several rows.
Term
linear combination
Definition
a sum of scalar multiples of vectors. The scalars are called weights
Term
scalar
Definition
a real number used to multiply either a vector or a matrix
Term
weight
Definition
the scalars used in linear combinations
Term
Homogenous system of equations
Definition
an equation of the form Ax=o possibly written as a vector equation or as a system of linear equations
Term
trivial solution
Definition
The solution x=0 of a homogenous equation Ax=0
Term
non-trivial solution
Definition
A non zero solutoin of a homogeneous equation or system of homogeneous equations
Term
parametric form of a solution set
Definition
Term
Linear Transformation
Definition
Term
transformation function, mapping
Definition
Term
linear transformation
Definition
Term
domain
Definition
The set of all vectors x for which Tx is defined
Term
codomain
Definition
the set Rm that contains the range of T/ In general if T maps a vector space V into vector space W, then W is called the codomain of T
Term
range
Definition
The set of all vectors of the form T(x) for some x in the domain of T.
Term
image
Definition
The vector T(x) assigned to x by T
Term
preimage
Definition
Term
shear
Definition
Term
contraction
Definition
A mapping x-->rx for some scalar r, with 0
Term
dilation
Definition
Term
reflection
Definition
Term
rotation
Definition
Term
standard basis vectors
Definition
Term
standard matrix for a linear transformation
Definition
the matrix A such that Tx = Ax for all x in the domain of T
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