Matrix Theory/ Isometries

Suppose A is a unitary matrix. (a) Show that there exists an orthonormal basis B of eigenvectors for A. (b) Let P be the associated change-of-basis matrix. Explain how to alter B such that P lies in SU(n).

Matrix Theory

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Matrix Theory

Prove that for in H, Thus, N is a homomorphism from onto the positive real numbers. See attached file for full problem description.

Finding the standard deviation from a coin toss.

A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed.

Find the probability

The Gray Stone Rock Band will give 10 performances this season.Four of these will be only songs from the 70s. If Tony gets to pick two tickets at random, what is the probability that he will get both 70s tickets?

Finding the probability of marbles drawn without replacement.

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability. The first marble is red and the second marble is white.

Determining the probability from a given situation.

Two distinct even numbers are selected at random from the first ten even numbers greater than zero. What is the probability that the sum is exactly 30?

Determining the probability from a given situation.

If two cards are drawn without replacement from a deck, find the probability that the second card is red, given that the first card was a heart.

Determining the probability that an event will not occur.

The probability that an event will occur is 0.2. What is the probability that the event will not occur?

Determining the probability from a given situation.

If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade.