matrix algebra

Question 1

rules for vector space

Answer 1

• given actor v and u in vector space V, then u+v are in V as well
• given vector v and real number a then a*v is also in V
• V is not empty, there is a zero vector 0v

Question 2

linear combination and relation

Answer 2

a1v1 + … + anvn - linear combination
a1v1 + … + anvn = 0 - linear relation
if a1 = … = an = 0 - tribal relation

Question 3

when list V is linear dependant ?

Answer 3

if there is a nontrivial relation, if it is trivial or det(A) != 0 V is linearly independent

Question 4

spanning set

Answer 4

it is every vector in V that can be written as linear combination of elements of V

Question 5

basis for the vector space V

Answer 5

it is a set U of elements of V that is linearly independent and spans V

Question 6

row rank and column rank

Answer 6

the dimensions of the row and columns spaces are referred to as the row and column rank