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

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 - 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

There is no life to be found in violence. Every act of violence brings us closer to death. Whether it's the mundane violence we do to our bodies by overeating toxic food or drink or the extreme violence of child abuse, domestic warfare, life-threatening poverty, addiction, or state terrorism.

Some guys lay their fannies out there every night - they play the game at such a high level, and they give so much that, frankly, they don't get credit for it. And I think it's tragic sometimes.

I felt different at 29 because 29, to me, is 30. There are times when I still feel like an actual toddler in a grown-up - well, semi-grown-up - body.

Articles themselves are condensed to narrow columns of text across 5, 6, 7 pages, and ads that are really distracting for the reader, so it's not a pleasant experience to 'curl up' with a good website.

When I feel there's a door open, you always walk through it.

Unspoken feelings are unforgettable.

When I first heard that song, it was a ballad but it had a lot more. It felt like a gospel song when I first heard it and it just moved me.

One thing I won't do in television is a sitcom. I find that world to be so neurotic and bizarre.

I've taken great pride in not being fragile.

Immersion in the scriptures is essential for spiritual nourishment

Adventure must be held in delicate fingers. It should be handled, not embraced. It should be sipped, not swallowed at a gulp.

Don't settle for anybody just to have someone. Set your standards. What kind of love do you want to attract? List the qualities you really want in the relationship. Develop those qualities in yourself and you will attract a person who has them.

I saw 'On The Town' about nine times. I discovered it. I loved it. I was in college.

I know it's an experience that I need to have if God's putting me through it.

What we've tried to do is have neighbors, colleagues, friends and family talking.

The commonality between science and art is in trying to see profoundly - to develop strategies of seeing and showing.

All facades fall sometime then the mask comes off and the real heart is seen.

The kind of job where you have to hustle and hustle and where you're not sure whether you will have enough clients next month, where you have less job security, is becoming much more common.

It's an honor to represent a Latin culture.

Don't let idiots ruin your day.

Vicious habits are so great a stain to human nature, and so odious in themselves, that every person actuated by right reason would avoid them, though he were sure they; would be always concealed both from God and man, and had no future punishment entailed upon them.

Integrity is the essence of everything successful.

I don’t sweat the small stuff.

Whatever state I am in, I see it as a state of mind to be accepted as it is.