Let | - || denote a family of vector norms and let I - las be a subordinate matrix norm. Show that ||A||M = max ||Ax|| [X]=1
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In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
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![Let | - || denote a family of vector norms and let
I - las be a subordinate matrix norm. Show that
||A||M = max ||Ax||
[X]=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F798c0733-c5ae-41c3-878c-41971c8a1cc1%2F45ec5fee-74d6-43b2-b16d-82d9f8cf329d%2Fmvtjg1.jpeg&w=3840&q=75)
As per the question we have to show that the alternative definition of the matrix operator norm i.e. ||A|| is :
||A|| = max||x|| = 1 ||Ax||
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