Karteikarten
Linear Algebra Test 1
Karten in diesem Stapel (24)
- 1Homogeneous System of EquationsA system where all the equations are equal to zero
3x-2y=0
4x+y=0 - 2Elementary Row Operationsscalar multiplication
addition
swapping - 3Row Equivalencerows are row equivalent if they are interreducible by elementary row operations
- 4Free variablevariables that are not leading variable and can take on any value in R
Leading variable can be expressed in terms of free variables - 5An m x n matrix over RA rectangular list of numbers with m rows and n columns
- 6Echelon formwhen the leading variable of each row is to the right of the leading variable of the above row
- 7Length of a vectorthe magnitude in physics
- 8Inner/Dot product of vectorsdot product in physics
- 9Axiom 1closure under vector addition:
v+ w is in V - 10Axiom 2vector addition is commutative:
v+w= w+v - 11Axiom 3Vector addition is associative:
(v+w)+u=v+(w+u) - 12Axiom 4There is a zero vector in V
v+0=v - 13Axiom 5Each vector has an additive inverse:
v+w=0 - 14Axiom 6V is closed under scalar multiplication:
rv is in V - 15Axiom 7scalar addition is distributive:
(r+s)v= rs + rv - 16Axiom 8scalar multiplication distributes of vector addition:
r(v+w)=rv+rw - 17Axiom 9Scalar multiplication is associative:
(rs)v=r(sv) - 18Axiom 10Multiplication by 1 is the identity operation:
1v=v - 19Check for if a subspace(S) is a vector spacecheck if r1s1 +r2s2 is in S
- 20Span of a subset of vector spaceThe set of all linear combinations of vectors from S
[S]=c1s1+...+cnsn
where the vectors sn are in S and c1 and c2 are real numbers in R - 21Linearly independent subset of a vector spaceif none of the elements are linear combinations of the other elements
Check for linear independence:
c1s1+...+cnsn=0
only if c1,...,cn =0 - 22Basis for a vector spacea sequence of vectors that is linearly independent and spans the vector space
- 23Standard basis for R^n En
- 24Dimension of a vector spacethe number of vectors in its basis
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- Karteikarten am Linear Algebra Test 1, erstellt von Sabrina Valcin am 08/03/2017.
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- Sabrina Valcin
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