Term
|
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
|
Definition
| The set of all linear combinations of v.....vp. Also the subspace spanned (or generated) b v1......vp |
|
|
Term
|
Definition
| a linear system with at least one solution |
|
|
Term
|
Definition
| a linear system with no solution |
|
|
Term
|
Definition
| a matrix whose entries are the coefficients of a system of linear equations |
|
|
Term
|
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
|
Definition
| two matrices for which there exists a finite sequence of row operrations that transforms one matrix into another |
|
|
Term
|
Definition
|
|
Term
|
Definition
| A reduced echelon matrix that is row equivalent to a given matrix |
|
|
Term
|
Definition
| the leftmost nonzero entry in a row of a matrix |
|
|
Term
|
Definition
| a position in a matrix A that corresponds to a leading entry in an echelon form of A |
|
|
Term
|
Definition
| A column that contains a pivot position |
|
|
Term
|
Definition
| any variable in a linear system that is not a basic variable |
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
| a list of numbers; a matrix with only one column. In general any element of a vector space. |
|
|
Term
|
Definition
| A matrix with only one column, or a single column of a matrix that has several columns |
|
|
Term
|
Definition
| A matrix with only one row, or a single row of a matrix that has several rows. |
|
|
Term
|
Definition
| a sum of scalar multiples of vectors. The scalars are called weights |
|
|
Term
|
Definition
| a real number used to multiply either a vector or a matrix |
|
|
Term
|
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
|
Definition
| The solution x=0 of a homogenous equation Ax=0 |
|
|
Term
|
Definition
| A non zero solutoin of a homogeneous equation or system of homogeneous equations |
|
|
Term
| parametric form of a solution set |
|
Definition
|
|
Term
|
Definition
|
|
Term
| transformation function, mapping |
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
| The set of all vectors x for which Tx is defined |
|
|
Term
|
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
|
Definition
| The set of all vectors of the form T(x) for some x in the domain of T. |
|
|
Term
|
Definition
| The vector T(x) assigned to x by T |
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
| A mapping x-->rx for some scalar r, with 0 |
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
| standard matrix for a linear transformation |
|
Definition
| the matrix A such that Tx = Ax for all x in the domain of T |
|
|
