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

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

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It is true that I have been studying both humility and pride for many years for the purpose of weakening pride in my own life and cultivating humility by the grace of God.

I am so clever that sometimes I don't understand a single word of what I am saying.

We were able to flood the zone immediately.

'Cyber-security' is one of those hot topics that has launched a thousand seminars and strategy papers without producing much in the way of policy.

I have been listening to the Stooges' self-titled first album for well over half my life, and it remains one of the most exciting and essential records I have ever had the good fortune to come into contact with.

School is a place that provides education and education is the key to life.

Fair treatment in the work force is no longer exclusively a labor issue, nor is it a women's issue - it is a fundamental economic issue.

He was distinguished for ignorance; for he had only one idea, and that was wrong.

Wearing colourful eyeliner in a graphic shape is the epitome of make-up as an accessory.

I would love to walk into a mall and see more than two or three stores that cater to women who are a size 14 and up!

It's sad that because I have one friend who is in the public eye, just being seen out together once means we're romantically involved. But I don't take it seriously, and it doesn't really affect me much.

My dream was to play for Alabama - football, basketball.

Everything that Traffic ever did, I'd give Steve a complete lyric, titled, written out with the verse, the bridge, the shape and rhyme and then Steve had to figure out how the meter of the words would fit musically.

The contemplation of truth and beauty is the proper object for which we were created which calls forth the most intense desires of the soul and of which it never tires.

I'm a huge fan of Taio Cruz. I'm really liking what he's doing at the moment. I'd love to do something with him.

I have Pro Tools on my computer, and I make CDs all the time.

Technological society has succeeded in multiplying the opportunities for pleasure, but it has great difficulty in generating joy.

You can discover more about a person in an hour of play than in a year of conversation.

Stimulus does not work.

I think it's very easy to get corrupted.

I think that the present is worth attention, one shouldn't sacrifice it to future conceptions of, of this future or that future.

Well, my background is journalism. I don't have any creative-writing experience except for one class I took as a sophomore in college.

It doesn't matter what temperature the room is, it's always room temperature.