Finite dimensional linear submanifold of N is complete.
Not what you're looking for?
Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold of N is complete and therefore closed.
Purchase this Solution
Solution Summary
This solution is comprised of a detailed explanation of the problem on a normed linear space.
It contains step-by-step explanation for the following problem:
Normed Linear Space:
Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold
of N is complete and therefore closed.
Solution contains detailed step-by-step explanation.
Solution Preview
Please see the attached file.
Suppose that is a normed linear space.
Let be a finite dimensional linear submanifold of .
Hence itself is a finite dimensional normed linear space.
Now we have to prove that is complete and therefore closed.
Let B = be a basis for so that
-------------------------------------(1)
...
Education
- BSc, Manipur University
- MSc, Kanpur University
Recent Feedback
- "Thanks this really helped."
- "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
- "Very nice thank you"
- "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
- "You are awesome. Thank you"
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.