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

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 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 don't like uncertainty. I don't play poker. I don't like bluffing.

Women have to air it out, hold on to it, work on it.

I don't know why people are so keen to put the details of their private life in public; they forget that invisibility is a superpower.

I love to shop at BCBG, because it's classy and elegant but a little bit sexy. It fits who I am in one store.

Even the best data security systems can't protect private taxpayer information from entrepreneurial foreign businesses than can make huge profits selling U.S. taxpayer information.

Dogs feel very strongly that they should always go with you in the car, in case the need should arise for them to bark violently at nothing right in your ear.

For a traveler going from any place toward the north, that pole of the daily rotation gradually climbs higher, while the opposite pole drops down an equal amount.

The structural thinking I use in the concert hall is unnecessary to most film projects, and most film composers make better use of the enormous range of pop and other materials and techniques required of them than I probably would, faced with the same challenge.

Dishonesty is so grasping it would deceive God himself were it possible.

Christianity, democracy, science, education, wealth, and the cumulative inheritance of a thousand years, have not preserved us from the vain repetition of history.

Doesn't anybody ever want to talk about anything else besides 'Star Trek?' There were 79 episodes of the series; there were 55 different writers. I was only one of them.

Higher costs naturally translate into fewer employers offering insurance coverage, and fewer employees accepting it, even when it is offered.

Expect the best, plan for the worst, and prepare to be surprised.

In Victorian England, people were told they should discourage their wives from reading because it would lead them into all sorts of devilish wickedness.

I will say that walking down the street, getting on the subway, taking the elevator, if there's one or two people and they say, 'Great job, Mayor,' that is a real turn-on. I mean, anybody that wouldn't find that satisfying, rewarding, exciting, thrilling - I think they should see the doctor.

Writing is no dying art form in America because most published writers here accept the wisdom and the necessity of encouraging the talent that follows in their footsteps.

When she started to play, Steinway came down personally and rubbed his name off the piano.

Keep it simple.

Imitation is the first instinct of the awakening mind.

Avoiding danger is no safer in the long run than outright exposure. The fearful are caught as often as the bold.

True enough, the Fed needs radical reforms. In particular, it needs to replace its failed forecasting models and be rid of the academics who overwhelm the Fed system.

When I was 19, I celebrated my first Valentine's Day while being in a relationship. I was so excited, but didn't know what the rules were. What should I get him, or was I even supposed to get him something?

I won't dispute that bankers' privileged treatment in the 2008 crash merits populist scorn. But unfortunately, without a bank bailout, there probably would have been a worldwide depression.

They always say that jazz doesn't sell, but it's a lie, because it does sell, and it sells consistently year in and year out.