Give a componentwise definition of a skew-symmetricmatrix

Linear Algebra and Differential Equations Lecture 3 Aim: Develop systematic approach to working with ordered sets of numbers (Rn = set of ordered n-tuples at real numbers x1, x2 … xn) BASICALLY, Rn is set of all real numbers Course convention: Elements of Rn will always be written as a column N = 1: number line N = 2: plane N = 3: 3D space For n > 3, can’t easily think about Rn geometrically ● Can add and scale vectors in Rn ● Addition and scalar multiplication of vectors in Rn satisfy familiar rules of arithmetic (commutative, associative properties) If vector x is in span of {v1, v2 … vk}, that means we can get to vector x in Rn by only travelling in the directions of {v1, v2, … vk} Note that 0 vector is always in span {v1, v2, … vk}, because they can be scaled by 0 = k Visual example of span: Key takeaways: Span = Everywhere we can get to in Rn travelling o​ nly in directions of the vector set. 0 is always in span. Linear Algebra and Differential Equations Lecture 3 Aim: Develop systematic approach to working with ordered sets of numbers (Rn = set of ordered n-tuples at real numbers x1, x2 … xn) BASICALLY, Rn is set of all real numbers Course convention: Elements of Rn will always be written as a column N = 1: number line N = 2: plane N = 3: 3D space For n > 3, can’t easily think about Rn geometrically ● Can add and scale vectors in Rn