Matrice remarquables - Matrice carrée, d'ordre n (n = p) - Matrice nulle : n x p, tous coeff = 0 - Matrice diagonale : matrice carrée, tous coeff en dehors diagonale = 0 - Matrice carrée unité, identitaire : diagonale à 1, reste à 0

Matrices - propriétés Propriétés - Dimension, taille, ordre : n x p - Coefficient, valeur, terme - on parle toujours ligne puis colonne - matrice carrée, diagonale de haut gauche vers bas droite

Matrices - addition - Commutative - Même dimension uniquement - Idem différence - multiplication par un nombre réel : commutatif, distributif

Matrices multiplication - simple - Matrice ligne par matrice colonne : nombre réel - Pour multiplier on doit avoir na = on

Matrice multiplication - propriétés - A x B = C - pa = nb - nc = na, pc = pb Exemple : A -> 2 x 4, B -> 4 x 6 C -> 2 x 6

Matrices multiplication - process cij = ai1 x b1j + ai2 x b2j + ... + ain x bpj

Matrices multiplication - propriétés - distributivité : À x (B + C) = A x B + A x C - non commutativité : A x B != B x A - puissance : A^n = A x A x A ... (n fois) - A^0 = I (ni = na) - inversibilite (m carrée) : A x A' = A' x A = I (matrice unité) (méthode à voir plus tard)

Élimination + back propagation Faire une élimination + back propagation sur un système 3 eq à 3 inconnues

Column multiplication On peut utiliser la multiplication en colonnes pour toute matrice :

Matrices élémentaires Ce sont les matrices qui représentent les étapes de substitution pour arriver à un système de n équations à n inconnues auquel on peut appliquer la back substitution.

Inversibilite Une matrice carrée de n coeff est invertible ssi elle possède n pivots

Transposé d'une matrice

I go out with a lot of British people. Some of them say I sound a little tipsy.

Value friendship for what there is in it, not for what can be gotten out of it.

I feel ups and downs are a part of ones career and this totally depends on how you take it. You can either be knocked down by the negative things or you can take it in a positive way and learn from it.

The Social Affairs Ministry and the police will continue to fight against the abuse of women and children. The ministry battles the harmful phenomenon of cults on a daily basis.

I'm very lucky with the people that recognise me - it's at a very tolerable level. I don't think I could handle the level of recognition which David Beckham has.

When you eat healthfully, your body gravitates relatively rapidly toward a better weight.

Reconciliation and forgiveness are matters of the heart. They cannot be forced on the people.

One key symptom of alcoholism is that the individual comes to need a drink for every mood--one to calm down, one to perk up, one to celebrate, one to deal with disappointment, and so on.

Nothing could be recorded in those days except by aiming a movie camera at the television screen. It was at least another 10 years before they had any kind of recording medium.

Whatever is dirty, it is women's job to clean up, or drive some man to clean up, and that goes for everything from cellar to senate.

Anything that's done to address unemployment in terms of massive stimulus spending is going to exacerbate deficits. And anything that's done to address deficits in the short-term is going to exacerbate unemployment.

I hate stories in which a person has an occupation and you never see him working at it, like all those marvelous Cary Grant movies where he's a surgeon, and you never see him in the operating room.

Goal setting has traditionally been based on past performance. This practice has tended to perpetuate the sins of the past.

I might have been born into a very literal sense of chaos, but in fact that state is true of all of us.

Integrity is incredibly important to me. As long as you're authentic, you can do no wrong.

The message I'm trying to send is that technology is political, and that many decisions that look like decisions about technology actually are not at all about technology - they are about politics, and they need to be scrutinized as closely as we would scrutinize decisions about politics.

Study the field that you want to get into and know everything about it.

I won't tolerate lying.

I've always had a love for making things my own.

Even if Koch Industries had a financial interest in the Keystone XL pipeline, what possibly could be wrong with that? Perhaps more important, under what circumstances would such an interest be worthy of a congressional inquisition?

We toured that record for a year, which turned out to be the culmination of ten years of being constantly on the road. We were sick to death of touring.

Change equals self-improvement. Push yourself to places you haven’t been before.

Don't listen to what anybody says except the people who encourage you. If it's what you want to do and it's within yourself, then keep going and try to do it for the rest of your life.

You ask me a question, I'm going to give you an honest answer.