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

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

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

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've been building slow, step by step.

All the colleges I played, most of the colleges, they were white.

I always have a good quality extra virgin olive oil. A cheap quality oil will end up cheapening your dishes. And I love sweetening my dishes with maple syrup. It has a bit of a bitter kick at the end that works wonderfully in savory dishes.

I don't worry anymore about where's the big hangout Tuesday night, Friday. Couldn't tell you and no one comes to me for advice anymore in those areas anymore, so real boring I would say.

Senator Douglas was very small, not over four and a half feet height, and there was a noticeable disproportion between the long trunk of his body and his short legs. His chest was broad and indicated great strength of lungs.

Service drives a lot of my decisions.

I would not go so far as to say that the French trade unions attached greater importance to the struggle for peace than the others did; but they certainly seemed to take it more to heart.

My music is really about people connecting with their identities, even if they aren't Jewish.

So many objections may be made to everything, that nothing can overcome them but the necessity of doing something.

I went from somebody who didn't sing to somebody who didn't speak.

Having a dance background, I became used to rejection at an early age. Dance is very competitive, especially for a sensitive person like me. But I realized it's better not to take it so seriously. If you beat yourself up, it's hard to keep going.

I feel so gratified about having finished college. I learned how to articulate myself. It gave me confidence more than anything. And also the ability to analyze the text.

My father always cooks more polenta than he needs for a meal. The excess he spreads on an oiled surface and chills. Next day, he cuts out chunks, fries them in olive oil and serves with salad.

Chess is as elaborate a waste of human intelligence as you can find outside an advertising agency.

In the summer of 1902, I was able to erect two experimental stations on two forts at Strasbourg for the purpose of closer study.

I am as ever a poor sinner a captive of eternal love running by the side of His triumphal chariot and I have no desire to be anything else as long as I live.

Invitation is the sincerest flattery.

I believe in nothing, everything is sacred. I believe in everything, nothing is sacred.

People are in such a hurry to launch their product or business that they seldom look at marketing from a bird's eye view and they don't create a systematic plan.

There's something about a holiday that isn't all about how much money you spend.

God shapes the world by prayer. The more praying there is in the world the better the world will be, the mightier the forces against evil.

Reducing the price of cancer drugs is a humanitarian move.

You don't have to be a chef or even a particularly good cook to experience proper kitchen alchemy: the moment when ingredients combine to form something more delectable than the sum of their parts. Fancy ingredients or recipes not required; simple, made-up things are usually even better.

When you start something new, you can be sure that the first few years will be full of failures and disappointments.