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)

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

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 - 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

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

First they ignore you, then they laugh at you, then they fight you, then you win.

Tomorrow never comes

The right to a trial is a core principle of the American legal system. Depriving Americans of these essential liberties undermines the Constitution while doing nothing to strengthen our national security.

Well, I'm a slow writer. For me, a good day is a page, maybe a page and a half. I'd love to be more efficient, but I am not.

Well, jazz is to me, a complete lifestyle. It's bigger than a word. It's a much bigger force than just something that you can say. It's something that you have to feel. It's something that you have to live.

I've been coaching the sport for a number of years. And I went through many athletes. Some athletes stay with your program for a long, long period of time. Some athletes, they have a different approach as far as coaching style or your philosophies. I totally respect their own opinions - they have the right to choose their own coach.

He alone sees truly who sees the Lord the same in every creatureseeing the same Lord everywhere he does not harm himself or others.

People call me a feminist whenever I express sentiments that differentiate me from a doormat or a prostitute.

We should recognize that nationalism does not mean discriminating against people of a different nationality. It simply means not allowing such people to seize our political power, for only when we Han are in control politically do we have a nation.

I'll give you my worst nightmare. I'm dreaming that I'm onstage, the curtain goes up, and I have no idea what my lines are or what's going on. I think I should know, I kind of know, I remember rehearsing... and the audience is there waiting.

I grew up in the D.C. area, and I used to wear a Redskins jersey just walking around. I just had kind of a bowl haircut for a long time and no sense of style or personal hygiene. But the main thing was the haircut. You know, when you see a haircut of yourself from around 12 or 13, it's rough. I also had really bad acne.

Defeat the fear of death and welcome the death of fear.

English is necessary as at present original works of science are in English. I believe that in two decades times original works of science will start coming out in our languages. Then we can move over like the Japanese.

Right now, my daughter's just rolling her eyes at everything I do; I'm just an embarrassment.

No one wants to die, and no one wants to die poor. These are the two fundamental truths that transcend culture, they transcend politics, they transcend economic cycles.

Life is tough, but so are you.

Coming from New York, you're kind of indoctrinated with anti-L.A. sentiment, but California is just a really dope state.

You can miss someone that died, you can miss someone that moved away, but the worst way to miss someone is to see them everyday.

Nothing is black-and-white, except for winning and losing, and maybe that's why people gravitate to that so much.

We love a tale of heroes and villains and conflicts requiring a neat resolution.

Before a negotiation can proceed and be completed, what is outside the scope of negotiation needs to be agreed.

I really don't know where my interest in death comes from. Maybe I've just got a twisted imagination. The truth is, I haven't had a hugely eventful life - maybe I'm compensating in my creative life. Or maybe I'm just a bit sick.

I am proud of the fact that my wealth is completely transparent.

In fashion, only sexy won't go out of fashion.