Quick Question: Is this matrix an orthogonal projection?

AI Thread Summary
The matrix P is analyzed for orthogonality in terms of its null space and range. It is determined that the range is spanned by the vector [0, 1], while the null space is spanned by the vector [1, -1]. Since these two vectors are not perpendicular, the matrix does not represent an orthogonal projection. Therefore, the conclusion is that the matrix P is not an orthogonal projection. The discussion effectively clarifies the conditions for orthogonal projections in relation to the given matrix.
mistymoon_38
Messages
18
Reaction score
0
[SOLVED] Quick Question: Is this matrix an orthogonal projection?

Homework Statement


P=[0 0 ]
[11]


Homework Equations





The Attempt at a Solution



Its orthogonal if the null space and range are perpendicular.
Range=[0 ]
[x+y]
null space=[x
 
Physics news on Phys.org
null space=[x ]
[-x]??
So then its not orthogonal??
 
If you mean the range is spanned by the vector [0,1] and the null space is spanned by the vector [1,-1] (which I think you do mean) then yes, not orthogonal.
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Trying to understand the logic behind adding vectors with an angle between them'

Thread 'Trying to understand the logic behind adding vectors with an angle between them'

My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
View full post »

Similar threads

Write the matrix representation of the raising operators....
Replies
6
Views
2K
I Finding the orthogonal projection of a vector without an orthogonal basis
Replies
3
Views
4K
I Proof concerning the Four Fundamental Spaces
Replies
14
Views
2K
Advice on calculating the determinant for 3x3 Matrix by inspection
Replies
2
Views
2K
Optimizing Null Space Solutions: How to Remove Zeros in Rank Deficient Matrices
Replies
10
Views
1K
Orthogonal projection over an orthogonal subspace
Replies
9
Views
2K
Why is AB an Orthogonal Projection Matrix?
Replies
3
Views
2K
Why Isn't My EM Stress Tensor Calculation Giving the Expected Result?
Replies
3
Views
1K
Find the probability of energy value after a given measurment
Replies
1
Views
2K
Projectile motion -- Maximum range it can travel inside a 2m tunnel
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top