1-2 Vector and matrix norms

Link to slides: www.dropbox.co...
In this video we show how you can
- Find 1-, 2- and ∞-norms of vectors
- Classify matrices as symmetric, antisymmetric, normal and orthogonal
- Use a vector norm to define an induced matrix norm
- Show that the Frobenius norm is not induced by a vector norm

[@wilsonailen5015]

please, can you send me a link to find the gradient(derivative) of norms? thank you

[@martijnanthonissen]

You probably need the derivative of the 2-norm? I think you can find that yourself! Just try differentiating its definition in components

[@MathematicsMadeSimple1]

Easy to follow, thanks!

[@yusramonem4482]

Thank you so much. I found the best explanation for an upcoming presentation.

[@anoushkabarthakur2314]

Hi sir, how would you show that induced matrix norms are sub-multiplicative?

[@martijnanthonissen]

Sorry for the delay! I forgot about your question. You can find a proof here: math.stackexchange.com/questions/435621/show-that-the-operator-norm-is-submultiplicative

[@yasir9909]

Sir, how could we compute L-1/L-infinity Mixed induced matrix and vector norms?

[@martijnanthonissen]

You may find this useful: nhigham.com/2021/10/12/what-is-a-matrix-norm/

[@yasir9909]

@@martijnanthonissen Thank you, Sir, your lectures are good for learning fundamental concepts of Linear Algebra.
Actually, I am trying to understand the introduction of sparsity in control signals through the use of L1 and L0 Norms...