cours/Excalidraw/matrice d'une forme bilinéaire 2023-01-23 19.58.05.excalidraw.md

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a591d364390b5f4b369bdb1ee208bf278d7b5510: f((x_1, x_2, \dots,x_{n}), (y_1,y_2,\dots,y_{n})) = \begin{pmatrix}x_1&x_2&\cdots&x_{n}\\\end{pmatrix} \times \begin{pmatrix}a_{1,1}&a_{1,2}&\cdots&a_{1,n}\\ a_{2,1}&a_{2,2}&\cdots&a_{2,n}\\ \vdots&\vdots&&\vdots\\a_{n,1}&a_{n,2}&\cdots&a_{n,n}\end{pmatrix} \times \begin{pmatrix}y_1\\ y_2 \\ \vdots \\ y_{n}\end{pmatrix} c50ea2d019e031caa193fa63cf5b539050a7eb83: \begin{pmatrix}y_1\\ y_2 \\ \vdots \\ y_{n}\end{pmatrix} f11744db28f09b44c3948aadbcf9b9ae5f9198bc: \begin{pmatrix}a_{1,1}\times y_1 + a_{1,2}\times y_2 + \cdots + a_{1,n}\times y_{n}\\a_{2,1}\times y_1 + a_{2,2}\times y_2 + \cdots + a_{2,n}\times y_{n}\\ \vdots\\a_{n,1}\times y_1 + a_{n,2}\times y_2 + \cdots + a_{n,n}\times y_{n}\end{pmatrix} b90cb8023965c18bfd646256d274b041d326fc52: \begin{pmatrix}x_1&x_2&\cdots&x_{n}\\\end{pmatrix} 63ceeb3d0b0ae1f262ef076176cc134307747a9c: +.\times da57028d7dc46b884561654eb2199580ed3db5ce: +.\times 5d36f9fcc7f28d5aa03103db2011400f5cfc797b: +.\times 5fef90e53187ecc7d5d3f9e0d2451a0f5d5ac685: +.\times c2a33daf507038ffaeee29f3d2e26493e8b08419: +.\times cb0e9620f7dc62a9bc84a87d43964cfbd9649b14: +.\times b1ba0d5f89cc11323887587f16eaa6dd8cabaca6: = \big(a_{1,1}x_1y_1 + a_{1,2}x_1y_2 + \cdots + a_{1,n}x_1y_{n}\big) + \big( a_{2,1}x_1y_1 + a_{2,2}x_1y_2 + \cdots + a_{2,n}x_1y_{n} \big) + \cdots + \big( a_{n,1}x_1y_1 + a_{n,2}x_1y_2 + \cdots + a_{n,n}x_1y_{n} \big) c1a024e8189b35441276e565da393989720cf9c8: = \displaystyle\sum\limits_{i=1}^{n} \sum\limits_{j=1}^{n} \Big(a_{i,j}x_{i}y_{j}\Big)

%%

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