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

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

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 believe in the American Dream, because I've lived it.

For me, prayer is not so much me setting out a shopping list of requests for God to consider as it is a way of 'keeping company with God.'

I'm a huge fan of 'Geordie Shore.' I watch it, and it's just my guilty pleasure. I sit there and can't believe what they are like. However, I have met all the girls, and they are lovely.

People do not want politicians they know to be corrupt.

I would rather live my life as if there is a God and die to find out there isn't, than live as if there isn't and to die to find out that there is.

I have never considered myself anything other than an environmentalist. I have spent the better part of my life either in the wilderness, or trying desperately to get there.

When credit is cheaper to use and easier to arrange, people do use more of it.

Prosecutors are all used to persons who commit fraud making wild accusations when they're caught.

Men are cruel but Man is kind.

Being exposed to different production environments in Korea, Japan and the U.S. was a great experience, and each system allows you to quench your thirst in a different way.

I wanted to make people happy, if only for an hour.

Actions speak louder than words. All companies say they care, right? But few actually exercise that care.

Brad Pitt's role in 'Mr. & Mrs. Smith' - I want to do that so bad! That's one of my favorite movies of all time, and that character was so funny.

Never rush into the waiting arms of the first person who seems to like you. That is not seduction but insecurity.

I've had deals over the years where I just haven't had good chemistry with the person across the table from me, so I've said to one of my brothers, 'You know what, you will be more effective than I will.' And that takes a level of confidence.

The father's greatest folly is that he believes he can be a much more simple person than he is; he is not really able to deal with his own complexity as a human being.

I do understand my limitations as a fiction writer, which is why my novels are always going to be close to home.

When you're filming, you work 19-hour days, and you know more about what's going on with your crew and co-workers than you do with your husband.

I set forth a humble and inglorious life; that does not matter. You can tie up all moral philosophy with a common and private life just as well as with a life of richer stuff. Each man bears the entire form of man's estate.

I think that the core doctrines of Christianity - the incarnation, the resurrection, life after death-these are as strong as ever. In fact, the belief in life after death has increased in this century.

I didn't defraud the government by taking money that was not mine.

Many young Muslims see no opportunities for themselves and do not feel they have control over their lives or a stake in their nation's future. Such pessimism leads to disengagement. We risk losing a generation of young Muslims to apathy and extremism.

It is terrible to see someone being beaten up by the English language.

I was rather a poor student, too easily distracted - did a lot of gazing out of windows, fine for training to be a writer, but not a great way to achieve in the classroom. The truth is that I was happy to bumble along and do enough to avoid detention, but not much more.