Inversibilite Une matrice carrée de n coeff est invertible ssi elle possède n pivots

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.

Transposé d'une matrice

I used to have acne when I was a kid growing up. You can imagine how serious that was in making you feel bad. And I had skinny bow legs. I mean, as a kid growing up, I was an insecure fella.

I had no friends. I worried a lot.

Reject cynicism. Reject certitude. And don't be a jerk. Be a good guy.

Despite the success cult, men are most deeply moved not by the reaching of the goal but by the grandness of the effort involved in getting there - or failing to get there.

The American flag is an enduring symbol of liberty, democracy, and justice. It is fitting that the House act to protect it as we approach our nation's birthday, and as our men and women in uniform rally behind it in Iraq's battlefields.

In moments of surprise we catch at least a glimpse of the joy to which gratefulness opens the door.

These days I'm mostly familiar with two parts of L.A.: one is movie culture, and the other is Asian culture. The Westside is work, and the Eastside is Chinese - which means my friends.

Cultivate peace of mind which does not separate one's self from one's surroundings. When that is done successfully, then everything else follows naturally.

Writing always means hiding something in such a way that it then is discovered.

Comedians get jokes offered to them, rock stars get women and underwear thrown onstage, and I get guys that want to take me fishing.

Being mindful means that we suspend judgment for a time, set aside our immediate goals for the future, and take in the present moment as it is rather than as we would like it to be.

Water and sanitation has not had the same kind of champion that global health, and even education, have had.

Even when they're not causing injury, human-controlled cars are often driven inefficiently, ineptly, antisocially, or in other ways additive to the sum of human misery.

An eye for an eye, and the whole world would be blind.

Poetry isn't a profession, it's a way of life. It's an empty basket; you put your life into it and make something out of that.

Like gravity, karma is so basic we often don't even notice it.

I still have to work on my weight and some of my other demons.

People write memoirs because they lack the imagination to make things up.

Boats are something I am very, very passionate about; cars are something I grew up with... I used to race cars since I was a child.

I don't have a Pollyana attitude toward life that claims everything is lovely.

I've heard from pre-K and kindergarten teachers alike that the Common Core is inappropriately pushing written literacy standards when the focus should be on the development of oral literacy skills. And that's actually delaying the development of literacy.

Wealth and want equally harden the human heart.

I feel like I've always been a full-time historian, but nobody knows it.

I used to have a real passion for writing, but not so much anymore - probably because I do too much of it.