ALGEBRAIC APPROACH TO TROPICAL - Math-Wiki
... and < interchanged. When the partial order is total, we just call it an order. A chain is a poset in which the given partial order is total. A lattice is a poset in which every pair {a, b} of elements has a supremum (sup) a ∨ b and an infinum (inf ) a ∧ b. In other words, a ∨ b ≽ a and a ∨ b ≽ b, but ...
... and < interchanged. When the partial order is total, we just call it an order. A chain is a poset in which the given partial order is total. A lattice is a poset in which every pair {a, b} of elements has a supremum (sup) a ∨ b and an infinum (inf ) a ∧ b. In other words, a ∨ b ≽ a and a ∨ b ≽ b, but ...
![Math 110B HW §5.3 – Solutions 3. Show that [−a, b] is the additive](http://s1.studyres.com/store/data/017359919_1-72a70245febeadd05992d7dba1b6dd48-300x300.png)
MATH10212 Linear Algebra Lecture Notes Textbook
... If the product Ax is defined then the ith entry in Ax is the sum of products of corresponding entries from the row i of A and from the vector x. Theorem 1.4.5: Properties of the matrix-vector product Ax. If A is an m × n matrix, u, v ∈ Rn , and c is a scalar, then (a) A(u + v) = Au + Av; (b) A(cu) = ...
... If the product Ax is defined then the ith entry in Ax is the sum of products of corresponding entries from the row i of A and from the vector x. Theorem 1.4.5: Properties of the matrix-vector product Ax. If A is an m × n matrix, u, v ∈ Rn , and c is a scalar, then (a) A(u + v) = Au + Av; (b) A(cu) = ...
