Matrices - addition - Commutative - Même dimension uniquement - Idem différence - multiplication par un nombre réel : commutatif, distributif — Résumé en image

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 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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Human beings have speculated about the relationship between inspiration and insanity for centuries.

The Memorial Finder covers the gap. It tells you the specific panel and number where you can find an individual but begins to reveal the connections between the names themselves. As you move around the site itself, a smartphone app will reveal adjacencies as well as the stories behind the names.

It was hard to be away from home, but I am glad that I am home now.

Once food gets into our fridges, larders and kitchens, ensuring that it gets used up before going off seems like an obvious thing to do - but it's alarming how many millions of tonnes are simply chucked because we don't keep track of the food we've spent our money on.

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But I think Hillary Clinton is one of the most amazing women of this time.

In a small room one does not say what one would in a large room.

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Reading has always been the great love of my life.

Some people want to advertise their weirdness, and spread it out, that's not me.

Reading is to the mind, what exercise is to the body. As by the one, health is preserved, strengthened, and invigorated by the other, virtue which is the health of the mind is kept alive, cherished, and confirmed.

It occurred to me that at one point it was like I had two diseases - one was Alzheimer's, and the other was knowing I had Alzheimer's.

An exorcism is tantamount to a miracle - an extraordinary intervention of God.

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I wanted to be a teacher.

When you share your last crust of bread with a beggar, you mustn't behave as if you were throwing a bone to a dog. You must give humbly, and thank him for allowing you to have a part in his hunger.