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Status: Tags: #cards/math232 Links: Math 232 Course Outline

MATH 232 Vocabulary

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1.1

$R^2$ ;; 2D space

$R^3$ ;; 3D space

n-tuple ;; ordered list of an numbers enclosed in brackets

coordinate ;; n-tuple that describes position of joint

scalar ;; object that can be described by a number, written normally

vector ;; object that can be described by a number value (magnitude) and direction. Can also be descripbed by n-tuple Components ;; each item of a vector

1.2

trivial solution ;; the solution that consists of the trivial solution ;; the solution that consists of the zero vector.
unit vector ;; a vector of length 1.
standard basis vectors in R2 ;; {e1 = (1, 0), e2 = (0, 1)} standard basis vectors in R3 ;; {e1 = (1, 0, 0), e2 = (0, 1, 0), e3 = (0, 0, 1)} linear

basis ;; a minimum spanning set.

1.3

length/magnitude/norm of vector ;; how long vector is angle of a vector ;; angle between x axis and vector, measured counter-clockwise

product ;; multiplication of two things

dot product ;; type of vector multiplication cross product ;; type of vector multiplication used only in $R^3$

orthogonal ;; at right angles, perpendicular

normal vector ;; vector orthogonal to what it is being referenced to/plane

1.5

Scalar Product ;; another name for the dot product (the result of the dot product is a scalar)

Inner product ;; another name for the dot product. Projection ;; an everyday example of this is your shadow - a projection of you onto the ground.

Unit Vector ;; a vector with a norm of 1

Dimension of a space ;; the number of vectors in the basis that spans the space. Hyperplane ;; n-dimensional generalization of the plane. A subspace whose dimension is one less than the ambient space. Triangle inequality ;; Diagonal of a rectangle is never longer than the sum of both sides

Cauchy-Schwartz Inequality ?

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2.1- Systems of Linear Equations and Elimination

Linear equation ;; equations of the form $a_1x_1 + a_2x_2 + … + a_nx_n = b$, geometrically a hyperplane in $R^2$

Homogeneous linear equation ;; linear equation where b is zero

Non-linear equation ;; all the rest

System of equations ;; a set of equations in the same variables Unknowns ;; the variables in a system of equations Solution ;; the values of the variables that solve the Solution set ;; the set of all the solutions

Consistent ;; a system of linear equations that has at least one solution Inconsistent ;; a system of linear equations that has no solution

Pivot ;; top non-zero entry in a column of a matrixs

2.4

Hooke’s Law ;; F = kx where F is force, k is the spring constant, and x is displacement.

Law’s of Electrical Circuits ;; Ohm’s Law, Kirchhoff’s voltage and current laws.

Flow Network ;; a collection of branches through which something flows. Partial Fractions ;; a method of rewriting a rational fraction as a sum of fractions whose denominators are linear or irreducible quadratic factors.

Chemical Equation ;; Indicate how reactants are rearranged into products. Balanced Chemcial Equations ;; Chemical Equations where both sides of the equation have the same number of atoms of each type.

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3.4

Range ;; set of all possible outputs of a transformation Nullspace ;; all of the inputs that get mapped to 0 Column space ;; subspace spanned by columns of a matrix Row space ;; the subspace spanned by rows of a matrix

3.5

Invertible ;; has an inverse I ;; multiplicattive identity matrix Additive identity ;; Adding 0 Additive inverse ;; y where x+y = 0, x is some number Multiplicative inverse ;; y where xy = 1, x is some number

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list from MATH 232 Vocabulary AND !outgoing(MATH 232 Vocabulary)

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Created:: 2022-01-10 13:02