Flashcards
MATH 307 Ch 1, 2.1, 2.2
Cards in this deck (31)
- 1linear system of equations
- 2solution of linear system of equations
- 3consistentA system of equations is consistent if there exists at least one solution of the system.
- 4inconsistentA system of equations is inconsistent if there exist no solutions to the system.
- 5unique solutionA solution is unique if it is the only solution to the system
- 6augmented matrix
- 7row-echelon form
- 8reduced row-echelon form
- 9pivot
- 10pivot variableA variable in a linear system is called a pivot variable if the corresponding column
in the RREF of the augmented matrix of the system contains a pivot. - 11free variableA variable in a linear system is called a free variable if the corresponding column in
the RREF of the augmented matrix of the system does not contain a pivot. - 12underdeterminedAn m × n linear system is called underdetermined if m < n.
- 13overdeterminedAn m × n linear system is called overdetermined if m > n
- 14linear combination
- 15span
- 16standard basic vectors
- 17field
- 18vector space
- 19subspaceLet V be a vector space. A subset U ⊆ V is a subspace if U is itself a vector space,
with the vector space operations inherited from V .
This is equivalent to the requirement that U contain 0 and be closed under the formation of linear combinations. - 20linear mapLet V and W be vector spaces. A function T : V → W is called a linear map
it is additive and homogeneous:
- 21injectiveA function f : X → Y is injective or one-to-one if, whenever f(x1) = f(x2), it
holds that x1 = x2. - 22surjectiveA function f : X → Y is surjective if for every y ∈ Y , there is an x ∈ X so that
f(x) = y. - 23bijectiveA function f is bijective or is a one-to-one correspondence if f is both injective
and surjective. - 24eigenvalue
- 25eigenvector
- 26isomorphismLet V and W be vector spaces. An isomorphism between V and W is a bijective linear map T : V → W.
- 27isomorphicVector spaces V and W are isomorphic if there exists an isomorphism between V
and W. - 28invertibleA matrix A ∈ Mn(F) is invertible or nonsingular if there exists an inverse matrix to A.
- 29identity matrixThe n×n identity matrix In ∈ Mn(F) is the n×n matrix with ones on the diagonal
and zeroes elsewhere. - 30diagonal matrix
- 31matrix of a linear map
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- Linear Algebra Flashcards on MATH 307 Ch 1, 2.1, 2.2, created by Daniel Luo on 13/09/2019.
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