- #1

meemoe_uk

- 125

- 0

Duh, I can`t calculate matrix norms using the formula....

||A|| = max || Ax || where || x || = 1

This is how I try to calculate them, what am I doing wrong?

e.g. Find norm 2 of A

A = 1 1

0 1

First find A's eigen system....

Solve characteristic polynomial....

( 1 - k ) ( 1 - k )

k = 1 - eigen value of A

Get eigen vector....

A - k I = 0

0 1 = 0

0 0 = 0

eigen vector = 1

0

As || Ax || is at a maximum when x is A's eigen vector, we can now calculate ||A||.

Ax = 1 1 * 1 = 1

= 0 1 0 = 0

Therefore

|| A || = || 1 || = 1

|| 0 ||

Actual answer = 1.618

Bah. I can do it for norm 1 and infinity, but not any number inbetween. I'm not allowed to use that traspose matrix ,spectral radius formula. What's the secret??? Please help.

I can`t seem to display a matrix nicely on my post either. sos

||A|| = max || Ax || where || x || = 1

This is how I try to calculate them, what am I doing wrong?

e.g. Find norm 2 of A

A = 1 1

0 1

First find A's eigen system....

Solve characteristic polynomial....

( 1 - k ) ( 1 - k )

k = 1 - eigen value of A

Get eigen vector....

A - k I = 0

0 1 = 0

0 0 = 0

eigen vector = 1

0

As || Ax || is at a maximum when x is A's eigen vector, we can now calculate ||A||.

Ax = 1 1 * 1 = 1

= 0 1 0 = 0

Therefore

|| A || = || 1 || = 1

|| 0 ||

Actual answer = 1.618

Bah. I can do it for norm 1 and infinity, but not any number inbetween. I'm not allowed to use that traspose matrix ,spectral radius formula. What's the secret??? Please help.

I can`t seem to display a matrix nicely on my post either. sos

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