Let V be inner product space. Let e 1 </msub> , . . . , e

George Bray 2022-06-26 Answered
Let V be inner product space.
Let e 1 , . . . , e n an orthonormal basis for V
Let z 1 , . . . , z n an orthonormal basis for V
I have to show that the matrix represents the transformation matrix between e 1 , . . . , e n to z 1 , . . . , z n is unitary.
You can still ask an expert for help

Want to know more about Matrix transformations?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Bornejecbo
Answered 2022-06-27 Author has 19 answers
Regard the vectors in the orthonormal bases ( e 1 , . . . , e n ) and ( z 1 , . . . , z n ) as column vectors. Then let U e and U z be the matrices where the rows are the transposes of the column vectors e 1 , . . . , e n and z 1 , . . . , z n respectively. Then both U e and U z are unitary, and the matrix which maps between ( e 1 , . . . , e n ) and ( z 1 , . . . , z n ) is going to be given by U e U z 1 , which will be unitary because U e and U z are unitary.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-06-13
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.
A=[2359891121431727]
Find a nonzero vector in Nul A.
A=[3201]
asked 2021-09-18

Find an explicit description of Nul A by listing vectors that span the null space.
A=[154310121000000]

asked 2021-09-13

Assume that A is row equivalent to B. Find bases for Nul A and Col A.
A=[12511324515212045365192]
B=[12045005780000900000]

asked 2022-06-24
Let T 1 be a reflection of R 3 in the xy plane, T 2 is a reflection of R 3 in the xz plane. What is the standard matrix of transformation T 2 T 1 ?
Here's my thinking so far:
Since the standard matrix for reflections in xy is
[ 1 0 0 0 1 0 0 0 0 ]
Similarly, standard matrix for orthogonal projection in the xz plane is
[ 1 0 0 0 0 0 0 0 1 ]
I could multiply
[ 1 0 0 0 0 0 0 0 1 ] [ 1 0 0 0 1 0 0 0 0 ]
to yield
[ 1 0 0 0 0 0 0 0 0 ]
Could someone confirm for me if this is a valid approach?
asked 2021-12-16

Is division of matrices possible?
Is it possible to divide a matrix by another? If yes, What will be the result of AB if
A=(abcd)

B=(wxyz)?

asked 2021-03-02

Let T be the linear transformation from R2 to R2 consisting of reflection in the y-axis. Let S be the linear transformation from R2 to R2 consisting of clockwise rotation of 30. (b) Find the standard matrix of T,[T]. If you are not sure what this is, see p. 216 and more generally section 3.6 of your text. Do that before you go looking for help!

asked 2022-05-22
Linear transformation matrix derivation
A = [ 1 2 0 3 ] R 2 × 2
L :   R 2 × 2 R 2 × 2 ;   X A X
Find the transformation matrix with respect to the basis
B 1 = [ 1 0 0 0 ] ,   B 2 = [ 0 0 1 0 ] ,   B 3 = [ 0 1 0 0 ] ,   B 4 = [ 0 0 0 1 ]

New questions