Question

7. Show that if , is a characteristic root of an lamda
unitary matrix then so is
1/lamda​

Answer 1

Answer:

Since λ is the eigen-value of a n×n matrix A, we have

|A−λIn|=0

Also since A is a real orthogonal matrix,we have

AAT=ATA=In

So we can conclude that

|A−λ(AAT)|=0

Or,

|λA(1λIn−AT)|=0

Or,

|λA|⋅∣∣∣1λIn−AT∣∣∣=0

Or, since A is non-singular,

∣∣∣AT−1λIn∣∣∣=0

So, we can conclude that 1λ is an eigen-value of the matrix AT.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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