Question

Verify that similarity is an equivalence relation. (Note that if X and Y are nonsingular, then...

Verify that similarity is an equivalence relation. (Note that if X and Y are nonsingular, then so is their product XY.)

Homework Answers

Answer #1

That's easy...

Have a great day.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For each of the following, prove that the relation is an equivalence relation. Then give the...
For each of the following, prove that the relation is an equivalence relation. Then give the information about the equivalence classes, as specified. a) The relation ∼ on R defined by x ∼ y iff x = y or xy = 2. Explicitly find the equivalence classes [2], [3], [−4/5 ], and [0] b) The relation ∼ on R+ × R+ defined by (x, y) ∼ (u, v) iff x2v = u2y. Explicitly find the equivalence classes [(5, 2)] and...
Problem 57 on page 617 from Rosen) Consider the equivalence relation R = {(x, y)| x-y...
Problem 57 on page 617 from Rosen) Consider the equivalence relation R = {(x, y)| x-y is an integer} a. What is the equivalence class of 1 for this equivalence relations? b. What is the equivalence class of 1/2 for this equivalence relation?
Determine whether the given relation is an equivalence relation on {1,2,3,4,5}. If the relation is an...
Determine whether the given relation is an equivalence relation on {1,2,3,4,5}. If the relation is an equivalence relation, list the equivalence classes (x, y E {1, 2, 3, 4, 5}.) {(1,1), (2,2), (3,3), (4,4), (5,5), (1,3), (3,1), (3,4), (4,3)} If the relation above is not an equivalence relation, state that the relation is not an equivalence relation  and why. Example: "Not an equivalence relation. Relation is not symmetric" Remember to test all pairs in relation R
Let R = {(x, y) | x − y is an integer} be a relation on...
Let R = {(x, y) | x − y is an integer} be a relation on the set Q of rational numbers. a) [6 marks] Prove that R is an equivalence relation on Q. b) [2 marks] What is the equivalence class of 0? c) [2 marks] What is the equivalence class of 1/2?
Let A = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A as follows : For all...
Let A = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A as follows : For all x,y A, xRy <=> 3|(x-y) . Find the distinct equivalence classes of R(discrete math)
Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 + y^2= a^2...
Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 + y^2= a^2 + b^2. a) Prove S in an equivalence relation b) compute [(0,0)], [(1,2)], and [(-3,4)]. c) Draw a picture in R^2 representing these three equivalence classes.
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a)...
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S = {(y,x),(z,y),(x,z)} on {x, y, z}. a) Explain why R is not an equivalence relation. b) Explain why S is not an equivalence relation. c) Find S ◦ R. d) Show that S ◦ R is an equivalence relation. e) What are the equivalence classes of S ◦ R?
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x,...
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x, y) ∈ R if and only if x + 2 > y. For example, (4, 3) is in R because 4 + 2 = 6, which is greater than 3. (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
Consider the differential equation x2y''+xy'-y=0, x>0. a. Verify that y(x)=x is a solution. b. Find a...
Consider the differential equation x2y''+xy'-y=0, x>0. a. Verify that y(x)=x is a solution. b. Find a second linearly independent solution using the method of reduction of order. [Please use y2(x) = v(x)y1(x)]
Let X,Y be posets. Define a relation ≤ on X × Y by the reciepe:                ...
Let X,Y be posets. Define a relation ≤ on X × Y by the reciepe:                 (x1,y1) ≤(x2,y2) iff   x1 ≤ x2     in X   and y1 ≤ y2 in Y In Above example check that (X ×Y,≤) is actually a poset, It is the product poset of X and Y