Lecture notes for Section 5.5
... Big Idea: Polynomials are the most important topic in algebra because any equation that can be written using addition, subtraction, multiplication, division, integer powers, or roots (which are rational powers) can be solved by converting the equation into a polynomial equation. Looking at the patte ...
... Big Idea: Polynomials are the most important topic in algebra because any equation that can be written using addition, subtraction, multiplication, division, integer powers, or roots (which are rational powers) can be solved by converting the equation into a polynomial equation. Looking at the patte ...
List of Objectives MAT 099: Intermediate Algebra
... (v) Recognize the graph of a polynomial function from the degree of the polynomial. (vi) Combine like terms. (b) Section 5.4 (i) Multiply two polynomials, including binomials. (ii) Square binomials. (iii) Multiply the sum and difference of two terms. (iv) Evaluate polynomial functions. (c) Section 5 ...
... (v) Recognize the graph of a polynomial function from the degree of the polynomial. (vi) Combine like terms. (b) Section 5.4 (i) Multiply two polynomials, including binomials. (ii) Square binomials. (iii) Multiply the sum and difference of two terms. (iv) Evaluate polynomial functions. (c) Section 5 ...
Zeros of Polynomial Functions
... Once you have all the possible zeros test them using substitution or synthetic division to see if they work and indeed are a zero of the function (Also, use a graph to help determine zeros to test) It only test for rational numbers ...
... Once you have all the possible zeros test them using substitution or synthetic division to see if they work and indeed are a zero of the function (Also, use a graph to help determine zeros to test) It only test for rational numbers ...
BABY VERMA MODULES FOR RATIONAL CHEREDNIK ALGEBRAS
... As A is Z-graded this inherits a Z-grading from H0,c . It follows immediately from the PBW theorem that we have an isomorphism of vector spaces given by multiplication ShcoW ⊗ CW ⊗ Sh∗coW → Hc which we view as a PBW theorem for restricted Cherednik algebras. In particular we see dim Hc = |W |3 . Som ...
... As A is Z-graded this inherits a Z-grading from H0,c . It follows immediately from the PBW theorem that we have an isomorphism of vector spaces given by multiplication ShcoW ⊗ CW ⊗ Sh∗coW → Hc which we view as a PBW theorem for restricted Cherednik algebras. In particular we see dim Hc = |W |3 . Som ...
The Learnability of Quantum States
... A Hint of What’s Possible… Theorem [A. 2004]: Any n-qubit quantum state can be “simulated” using O(n log n log m) classical bits, where m is the number of (binary) measurements whose outcomes we care about. Let E=(E1,…,Em) be two-outcome POVMs on an nqubit state . Then given (classical description ...
... A Hint of What’s Possible… Theorem [A. 2004]: Any n-qubit quantum state can be “simulated” using O(n log n log m) classical bits, where m is the number of (binary) measurements whose outcomes we care about. Let E=(E1,…,Em) be two-outcome POVMs on an nqubit state . Then given (classical description ...
