under what conditions will a diagonal matrix be orthogonal?

Answers

Answer 1

A diagonal matrix can only be orthogonal if all of its diagonal entries are either 1 or -1.

For a matrix to be orthogonal, it must satisfy the condition that its transpose is equal to its inverse. For a diagonal matrix, the transpose is simply the matrix itself, since all off-diagonal entries are zero. Therefore, for a diagonal matrix to be orthogonal, its inverse must also be equal to itself. This means that the diagonal entries must be either 1 or -1, since those are the only values that are their own inverses. Any other diagonal entry would result in a different value when its inverse is taken, and thus the matrix would not be orthogonal. It's worth noting that not all diagonal matrices are orthogonal. For example, a diagonal matrix with all positive diagonal entries would not be orthogonal, since its inverse would have different diagonal entries. The only way for a diagonal matrix to be orthogonal is if all of its diagonal entries are either 1 or -1.

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Related Questions

30 people liked Brand X. This is 20% of the people in a survey.
a) How many people were there in the survey?
b) What percent of the people did not like Brand X?
c) How many people did not like Brand X?

Answers

a) 150 people
b) 80%
c) 120 people

Which side lengths represent the sides of a right triangle?
A)
1, 1, 2
B)
2, 3,5
C)
5, 12, 13
D)
7, 23, 25

Answers

Answer: the answer is C

Step-by-step explanation:

My friend is a math teacher

Hope this helps

A computer at an electronics store costs $2,893 The tax is 6% how much money will you spend total?

Answers

Answer:

$3066.58

Step-by-step explanation:

$2893 x 1.06= $3066.58

Hope this helps!

HELP DUE IN 10 MINS!!!

Jones is drawing a plan of a gate house. He is using a scale of 2cm to 5m. The entrance is
12.5m long. How long should he draw the entrance on his plan?

Answers

4? i’m not sure on this one

Identify the shape that is graphed from the points:
A (4, 6)
B (4, 7)
C (8, 6)
D (8, 7)

Answers

Answer:

Rectangle

Step-by-step explanation:

It's a rectangle because opposite sides are parallel as you can see , it has 4 right angles , and it has 4 sides .. it's not a square because in a square all sides are equal

Fill in the blanks
A
integers.
is an algebraic expression that contains a variable to the power of one.
is an example.
is a rational number that is multiplied by a variable. A
is a number that can be written as the ratio, or fraction of two
in the expression is an example of a coefficient
are terms whose variables and their exponents are the same. One example is
and -7y.
2y
Like-terms
4
6x+5
linear-expression
4z
rational-coefficient
rational-number

Answers

Answer:

Step-by-step explanation:

okay here’s the answers in order

Linear-expression

6x+5

rational coefficient

rational-number

Like-terms

Hi I need help can someone simplify this?

Answers

The simplified expression is c^5

Answer:

c^5

Step-by-step explanation:

Cameron picked two pairs of shorts and three T-shirts’ for a weekend trip. What are some combinations of shirts and shorts that Cameron can wear while on his trip? How many days will he have a different outfit to wear?

Answers

Answer:

Step-by-step explanation:

(yellow shirt, green shorts),

(yellow shirt, blue shorts),

(white shirt, green shorts),

(white shirt, blue shorts),

(orange shirt, green shorts),

(orange shirt ,blue shorts)

There is six options so he will have six days to wear different outfits. pls give brainliest, im new.

Simplify the expression. Drag and drop a number into each box to complete the simplification.

Answers

Answer:

The first one is 3, the second one is 9, the third box is 63 and the last box is 67

five yellow m&m for every 3 green. How many green m&m if there are 95 yellow ?
PLEASE HELP

Answers

For this problem, you need to set up a proportion. For every three green there are five yellow, so your first fraction is 3/5. For the second fraction, plug 95 into the denominator. You should have an equation of 3/5 = x/95, x being the number of green. After cross multiplying (95(3)/5), you should get an answer of 57 green. Hopes this helps!

3/10 divided by 2/5?

Answers

Answer:

3/4 is your answer

Step-by-step explanation:

Jeffrey walked 1/3 mile on Monday and jogged 4/5 mile on Tuesday. How far did he walk and jog on Monday and Tuesday combined?

Answers

18/15 because the like denominator is 15 and 1/3 is 5/15 and 4/5 is 12/15. Them added together is 18/15

Answer:

Jeffery walked 1.13 miles in total.

Step-by-step explanation:

1/3 and 4/5. To solve this problem, we need to find a common denomonator.

3 and 5

LCM = 15

1/3* 5/5

5/15

4/5 * 3/3

12/15

5/15 + 12/15 = 17/15

= 1.13

Me han descontado 10 euros en unos pantalones que estaban rebajados un 20 porciento .¿cuantos costaban los pantalones ?¿cuanto ha pagado por ellos ?

Answers

Answer:

los pantalones costaban 50 euros, y ha pagado 40 euros

What does probability mean?

Answers

Answer:

There you go

Step-by-step explanation:

Not much of an explanation but it works because I also don't know what meaning you want to it.

PLEASE HLEP
14.Write the expanded form of the expressions below: y(-3-7x)

Answers

Answer:

− 7 − 3

Step-by-step explanation:

( − 3 − 7 )

( − 7 − 3 )

Answers? And please explain

Answers

Use mathaway homie that works like a charm yurrr meh

What is 73 x 4 + 13?

Answers

Answer:

73 x 4 + 13 is 305

Answer:

305

explaination:

73 x 4 = 292

292 + 13 = 305

Proof that 1^√2 = 1 is true

Answers

Answer:

1^sqrt(2) = 1 is always true

Step-by-step explanation:

it is always 1 because the teacher said.....lol

6*10^5 is how many times as large as 3*10^3

Answers

Answer: 200 times larger

Explanation (6*10^5)/(3*10^3)=2*10^2

2*100=200

The other answer was wrong because in order of operations (PEMDAS), exponents come before multiplication.

Lorenzo's lovely lamp land buys a lava lamp for $24. They sell the lamp to the end customer for $50.40. What is the markup percent?

Answers

Answer:

110%

Step-by-step explanation:

100%->24

1%-> 0.24

50.40 -24 = 26.40

26.40÷0.24=110%

Need help ASAP pls help

Answers

Answer: The correct answers are B, D, and F.

Step-by-step explanation: B is correct because 8 x 5 is 40, and 40-5 is less than or equal to 36. C is correct because if you plug in 41/8, the answer is 36. Anything higher than 41/8 is greater than 36. F is correct because 5 is a solution and 5 is less than 41/8. Therefore, the correct answers are B, D, and F.

Please I need help with this?

Answers

9514 1404 393

Answer:

(a) positive and increasing

Step-by-step explanation:

Point c is on the x-axis, and point d is above it. The curve between points c and d is positive and increasing.

Pls help I really need this

Answers

Answer: 45 sq ft

Step-by-step explanation:

(9*10)/2 bc its a right triangle

90/2

1 pts
An adult blue whale can eat about 102,000,000 krill a day. Write this number in
scientific notation.

Answers

1.02 x 10^8 is the correct answerPlease let me know if I am wrong.

Pls help me on this question!!

Answers

Answer:

from what i can tell this seems to be a translation three units down and three units to the left, this is not a dilation

Step-by-step explanation:

Please help ASAP I need this right now

Answers

Answer:

You have to look closely and you will find The letters D and C on the bottom of the triangle. D is kinda on the right and C is on the left. Hope this helps.

Step-by-step explanation:

Hello! It would help a lot if I had assistance with this question:

Answers

The answer to this question is the third option 4 1/3

Answer:

4 1/3 is the answer.

Hope it helped!!

Given A=
What is the value of matrix B if A + B = C

Answers

Answer:

Step-by-step explanation:

We know that 8+3x= x

solve for x

8= -2x

-4 =x

The only answer that has -4 is A

The hotdog stand at a baseball game sells hotdogs for $3.50 each. The amount, D dollars, Mr. Moore paid for the hotdogs is directly proportional to the number of hotdogs, H, he buys. Identify the constant of proportionality and write a direc

Answers

Answer:

D α H

k = D/H

k = 3.50

Step-by-step explanation:

Amount paid, D is directly proportional to the number of hotdogs, H

D = $3.50 per hot dog

D = $3.50 is directly proportional to 1 hotdog

Hence,

D α H

D = kH

k = proportionality constant

H = 1

3.50 = k

k = 3.50

k = D/H

If you know the answer plz help

Answers

Answer:

I think that it will be (6)

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