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 - 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

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

Only a goalie can appreciate what a goalie goes through.

Broadway has changed tremendously from the early days when the shows were referred to as musical comedies. Musical Theater is now a more expanded art form. Back then, singer/actors were not the norm. From the 60's to now, it is necessary to do it all to be a consummate Broadway performer.

I'd say most of my songs I write from personal experience. When I feel like I don't have any inspiration in my personal life, I think about others that are close to me and maybe what they're going through or even just people I've come across, acquaintances.

I wake about 1 a.m. I'm in the office by 2 a.m. We're on the air at 5.

The pressure of survival in the big city will make you lose sight of your dream... Hang in there.

Traveling around the country, meeting fans and hearing their stories in person and on my radio show has reenergized my commitment to creating honest and inspirational content that not only serves my own creative purposes but can help and touch others as well.

I don't think I've met anyone with a stronger work ethic than Ray Charles.

If you're receiving fewer assignments, this could be an indicator that there was a decision from upper management that you shouldn't have as many responsibilities. Whether that means your employer has lost faith in you or that your job may be in jeopardy, this is a sign that you should start polishing up your resume.

Too much of what is called 'education' is little more than an expensive isolation from reality.

I don't care what people think or say about me, I know who I am.

Smart cities are those who manage their resources efficiently. Traffic, public services and disaster response should be operated intelligently in order to minimize costs, reduce carbon emissions and increase performance.

If you get the government off our back, there's no economy in the world that can create more jobs in the long-term for everybody.

In climbing you are always faced with new problems in which you must perform using intuitive movements and then later analyze them to figure out why they work and then learn from them.

Improvised music involves a lot of intuition and I like developing intuition.

When you feel like giving up remember why you held on for so long in the first place.

Once you establish a foundation of knowing what the greatest recording artists of all time were... Wouldn't you want your kids to know this stuff?

It was widespread that the politics of Tea Party people would be foreign to Ronald Reagan and they would be seen by him as frivolous and uninformed.

Art is a fruit that grows in man, like a fruit on a plant or a child in its mother's womb.

I have been through various fitness regimes. I used to run about five miles a day and I did aerobics for a while.

I have often heard the statement made by foreign singers, as a demonstrated fact, that the German artists are artists in feeling indeed, and serious in their devotion, but that their singing is crude.

I was 8 years old when I went across the street from my house to a fair, and they always had a used book sale. For a quarter I bought a book called 'Come On Seabiscuit.' I loved that book. It stayed with me all those years.

Just keep stirring the pot, you never know what will come up.

If you love epic space opera, you shouldn't miss 'Interstellar'.

We make the assumption that everyone sees life the way we do.