Subspace - Study guides, Class notes & Summaries

summary of spans, linear combinations, bases and dimensions

CONTENTS 1 Some Prerequisite Topics 1 1.1 Sets And Set Notation ................................... 1 1.2 Well Ordering And Induction ............................... 2 1.3 The Complex Numbers ................................... 4 1.4 Polar Form Of Complex Numbers ............................. 6 1.5 Roots Of Complex Numbers ................................ 6 1.6 The Quadratic Formula .................................. 8 1.7 The Complex Exponential ................................. 9 1.8 ...

MATH 5101: Linear Mathematics in Finite Dimensions Lectures: Summaries, Notes, and Text Books U. H. Gerlach Autumn 2015 Contents 1 VECTOR SPACES 6 1.1 Lecture 1 (Wednesday) . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.1 Three archetypical equations of linear algebra . . . . . . . 6 1.1.2 Vector as an aggregate of entities . . . . . . . . . . . . . . 6 1.1.3 Vector space: Denition and Examples . . . . . . . . . . . 6 1.1.4 Subspace of a vector space . . . . . . . . . . . . ...

We always denote by X our universe, i.e. all the sets we shall consider are subsets of X. Recall some standard notation. 2 everywhere denotes the set of all subsets of a given set X. If A B = ? then we often write A t B rather than A [ B, to underline the disjointness. The complement (in X) of a set A is denoted by A X . By A4B the symmetric difference of A and B is denoted, i.e. A 4 B = (A n B) [ (B n A). Letters i; j; k always denote positive integers. The sign ¹ is used for restr...

Span( V1,...,VP) set of all linear combinations Basis of a vector subspace Let H be a subspace of a vector space V. An indexed set B=(v1,...vp) in V is a basis for H if: (i) B is a linearly independent set (ii) the subspace spanned by B coincides with H, that is, H=span(v1,...,vp

Null Space Solution Space of a homogenous system Nullity Dimension of the Null space Dimension Number of vectors that form a basis. (non zero rows in a rref matrix Linearly dependent When the sum of subspace multiplied by a non-zero constant equals the zero vector Gram Schmidt Consistent has a solution Projection [(V,W1)/(W1,W1)]W1+[(V,W2)/(W2,W2)]W2....

Which of the following subsets of R33 are subspaces of R3x3.2

MATH: Differential Equations and Linear Algebra Question & Answer 10 Rules of Vector Spaces - ANSWER: Addition, Scalar Multiplication, Commutativity, Associativity, Zero Vector, Additive Inverses, Distributive Properties, and Scalar Identity Additive Inverses - ANSWER: U+(-U)=(-U)+U=0, you can add a vector to its inverse and get the zero vector Algebraic Dot Product - ANSWER: U (dot) V = U1V1+U2V2+...+UnVn Angle Between Vectors - ANSWER: theta=acos(U (dot) V)/(||U||*||V||) Associativity -...

Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 3.3 The Dimension of a Subspace of R^n 3.4 Coordinates

Linear Algebra with Applications (Fifth Edition) by Otto Bretsch 3.3 The Dimension of a Subspace of R^n 3.4 Coordinates