# Characteristic polynomial

### Explore related topics

For the minimal polynomial of an algebraic element of a field, see Minimal polynomial (field theory). In linear algebra, the minimal polynomial μA of an n × n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any other polynomial Q with Q(A) = 0 is a (polynomial) multiple of μA. The following three statements are equivalent: λ is a root of μA, λ is a root of the characteristic polynomial χA of A, λ is an eigenvalue of matrix A. The…

### Graphing Polynomial Functions Scavenger Hunt

Graphing Polynomial Function Scavenger Hunt Activity - This walk around activity will help students practice identifying the key characteristics of polynomial functions and connecting those characteristics to graphs. Students begin the activity by choosing any one of the graphs posted around the classroom, and the equation of that graph will lead them to the next station.

Properties of polynomial functions

### Algebra I 90 Question EOC Review

Includes 5 sets of 5 Solving Equation and Inequality Problems6 Graphing Linear Functions 5 Slope Problems3 Regression Problems 5 Solving Quadratic Equations5 Exponential Growth and Decay 12 Polynomials Problems5 Systems of Linear Equations 4 Simplifying Radicals3 Arithmetic/Geometric Sequence 5 Solving Literal Equations5 Linear Characteristics 5 Writing Linear Equations5 Quadratic Characteristics 5 Transformation Problems11 Exponent Problems 4 Writing Equations from Verbal…

Example of finding the characteristic polynomial and its factorization in a Diagonalization problem.

### Graphing Polynomial Functions Flip Book

Graphing Polynomial Functions Flip BookThis flip book was created to be used as a stations activity to provide extra practice with graphing polynomial functions and identifying the following key characteristics:Turning Points (Relative Minimum and Relative Maximum), Increasing Intervals, Decreasing Intervals, Parent Function, End Behavior, Zeroes, Domain, and Range.There are 8 functions in the book.

### PreCalculus: Polynomial Power and Rational Functions Stations Activity

This activity is designed to help your Pre-Calculus students review key concepts at the end of the unit on Polynomial, Power, & Rational Functions. There are 40 cards in the set. 10 graph cards have a corresponding equation card, zeros card, and characteristic card. Great fun while practicing difficult concepts.

A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic

Mathematics Made Easy: Multiplication

Using the game for characteristics of polynomials.