Definition. For any A∈ Mn×n(C), define the norm of A by ||A||= max{|Aij |: 1 ≤i, j≤n}.Let A,B∈ Mn×n(C). Prove the following results.(a)||A||≥0 and ||A||= 0 if and only if A=O.(b) ||cA||= |c| . ||A||for any scalar c.(c)||A+B||≤||A||+ ||B||.(d)||AB||≤n||A||||B||.

Question
1 views

Definition. For any A∈ Mn×n(C), define the norm of A by ||A||= max{|Aij |: 1 ≤i, j≤n}.

Let A,B∈ Mn×n(C). Prove the following results.

(a)||A||≥0 and ||A||= 0 if and only if A=O.

(b) ||cA||= |c| . ||A||for any scalar c.

(c)||A+B||≤||A||+ ||B||.(d)||AB||≤n||A||||B||.

check_circle

Step 1

Hey, since there are multiple sup-parts posted, we will answer first three sup-parts of the  question. If you want any specific sup-part to be answered then please submit that question and specify sup-part number in your message.

Step 2
Step 3

Want to see the full answer?

See Solution

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in