How it works

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. — Elles permettent d'obtenir les coefficients du système sous forme d'une matrice triangulaire U On passe de Ax = b à Ux = c

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Maths - Algèbre linéaire

Algèbre linéaire pour machine learning
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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
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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
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Matrices - addition - Commutative - Même dimension uniquement - Idem différence - multiplication par un nombre réel : commutatif, distributif
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Matrices multiplication - simple - Matrice ligne par matrice colonne : nombre réel - Pour multiplier on doit avoir na = on
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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
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Matrices multiplication - process cij = ai1 x b1j + ai2 x b2j + ... + ain x bpj
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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)
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Élimination + back propagation Faire une élimination + back propagation sur un système 3 eq à 3 inconnues
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Device:96a1806c ed21 4b75 a06c 437246c174a911602 ec2301.nx19ssjor
Column multiplication On peut utiliser la multiplication en colonnes pour toute matrice :
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Inversibilite Une matrice carrée de n coeff est invertible ssi elle possède n pivots
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Device:96a1806c ed21 4b75 a06c 437246c174a946292 v5jtc6.lurwg919k9
Transposé d'une matrice
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Traditional arguments for the existence of God and contemporary attempts to use fine-tuning and cosmology to back up the case for his existence always strike me as kinds of games, since hardly anyone believes on the basis of these arguments at all.
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I was lucky enough to have the talent to play baseball. That's how I treated my career. I didn't think I was anybody special, anybody different.
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Nobody ever drowned in his own sweat.
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Dont give up. Dont lose hope. Dont sell out.
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Your characters have to remain innocent of what your picture is after.
Douglas Sirk
Going to a party, for me, is as much a learning experience as, you know, sitting in a lecture.
Natalie Portman
When the Christians, upon these occasions, received martyrdom, they were ornamented, and crowned with garlands of flowers; for which they, in heaven, received eternal crowns of glory.
John Foxe
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As you reach your goals set new ones. That is how you grow and become a more powerful person.
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I just started writing for my own amusement and occasionally singing in little clubs around Los Angeles. Then I wrote 'The Rose,' and through a series of divine things that I had no control over and had no idea were going to happen, it got in the movie, and that changed everything.
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Romania and Bulgaria were particularly irresponsible. If they wanted to diminish their chances of joining Europe they could not have found a better way.
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