Wikipedia article Displaying a formula, which is actually about formulas in Math Markup.
.
\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

\begin{array}{rcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

\begin{array}{rcl} f: R^3 & \to & R \\ (x,y,z) & \to & x + y + z \\ f(x,y,z) & = & x + y + z \end{array}

\begin{array} {lcl} f(x) & = & (a+b)^2 \\ & = & a^2+2ab+b^2 \end{array}

.
f(n) = \begin{cases} n/2, & \mbox{if } n\mbox{ is even} \\ 3n+1, & \mbox{if } n\mbox{ is odd} \end{cases}

.
\begin{cases} 3x + 5y + z \\ 7x – 2y + 4z \\ -6x + 3y + 2z \end{cases}

.
\left| \begin{array}{cc} x_{11} & x_{12} \\ x_{21} & x_{22} \end{array} \right|

Matrix frames are provided by \left and \right. If you suppress these statements, it will be displayed like:
\begin{array}{cc} A & B \\ C & D \end{array}

However, there is another statement, the matrix declaration, slightly easier to use:
\begin{matrix} x & y \\ z & v \end{matrix}

The frames of the matrix can be displayed in several forms, by just changing the matrix declaration to vmatrix, Vmatrix, bmatrix, Bmatrix or pmatrix, as shown ahead:
\begin{vmatrix} x & y \\ z & v \end{vmatrix}

\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}

\begin{bmatrix} x & y \\ z & v \end{bmatrix}

\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}

\begin{pmatrix} x & y \\ z & v \end{pmatrix}

As a final example, let us construct more complicated matrices and matricial expressions:
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}

Now, we will show a first matricial expression:
\left[ \begin{array}{c} x_1 \\ x_2 \end{array} \right] = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \times \left[ \begin{array}{c} y_1 \\ y_2 \end{array} \right]
![\left[ \begin{array}{c} x_1 \\ x_2 \end{array} \right] = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \times \left[ \begin{array}{c} y_1 \\ y_2 \end{array} \right] \left[ \begin{array}{c} x_1 \\ x_2 \end{array} \right] = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \times \left[ \begin{array}{c} y_1 \\ y_2 \end{array} \right]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v8rffFNNK3q4eeS-Xb6cGXgSje2dbVX65LqF1MMa1ihKVbjOjnS9g6xQzmr2_6EcFU7lBAXlCJ6dPwqYJ6xwpq0ldVjNS1ih6QCZySHcsMIWq16PkgsgKM6sE5QgXTqL_fnX9MzZz93yhR7L_w_AxbY5IFfVPeCYWAnPhx2IZjU7aTjxti2A8dJWwQxQrT7BdUcN4nCgwJ0J1z4ac0Ko6f2ne7JTZefTSD7_gQkYQrjO6yYC_MF19XTGhgvaCJehuFhrGR9F2Xe78nRqU5S78fn5d2S8xpQDJS1mhRpHsNRdFTN-yvd0-2m347S8y_DkNjJ_H22t1Txd6QiPttssDzg-HVIwCbOLprYQyBjpdnWfSpB6GuyNsrbh_nSIgNm14KCZUyDA6E6yZaTd_ADt8QmcNkkPOpdAQMIKaF8o6F9K9bdBXMxS2INgelrph7yOmB8W3cAUNZOQ=s0-d)
and, here is another example, now using two kinds of vectors:
\begin{bmatrix} xz & xw \\ yz & yw \end{bmatrix} = \left[ \begin{array}{c} x \\ y \end{array} \right] \times \left[ \begin{array}{cc} z & w \end{array} \right]
![\begin{bmatrix} xz & xw \\ yz & yw \end{bmatrix} = \left[ \begin{array}{c} x \\ y \end{array} \right] \times \left[ \begin{array}{cc} z & w \end{array} \right] \begin{bmatrix} xz & xw \\ yz & yw \end{bmatrix} = \left[ \begin{array}{c} x \\ y \end{array} \right] \times \left[ \begin{array}{cc} z & w \end{array} \right]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_udUIoUV3yo7pI3WosfIhjAUG_xlCSIN_cOdyDRl8KcaHYFLLnJHirYdn35LV-J-VtauFXiW_pDnv_4CIeF7TO4QToNyCwaOBgYDIn_4NlRYXcFMd5t-xWimHtinwxkGRFV49K_HZAbe79Q3zJ7MGHsfa-Eue-e-IaL4fXofTKiHW1uql__FmwEhFUIAdPWVHsuRdJiF5I_A4T_jdpBdXzQrn-x477xLC6hgg_p9ZRE8eGIVb9iwa4YA0GUmB-FjfhDd4CKx0FImO9WqXE79c1nYpCvcJbu6bAPcOoqVGLdottYn1TcuDAdiSH2skBDkyI1sWSSORJCi5J3rHs70ymnnQa_3FBqnVU4RICiATgiZ6ijrLm55hoZw1cHGZKa2CpI1lTwmSr-Gnm5ENWMwhC-xL6n2sg5xhQLXX5VMfhA0QzLFR_uE8oUihxE=s0-d)
Many of the examples shown here were adapted from the .
Multiline Equations
You can present equations with several lines, using the array statement. Inside its declaration you must :- Define the number of columns
- Define column alignment
- Define column indentation
- Indicate column separator with & symbol &
\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}
\begin{array}{rcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}
\begin{array}{rcl} f: R^3 & \to & R \\ (x,y,z) & \to & x + y + z \\ f(x,y,z) & = & x + y + z \end{array}
\begin{array} {lcl} f(x) & = & (a+b)^2 \\ & = & a^2+2ab+b^2 \end{array}
.
Case definitions
Used when a definition have two or more cases. Use the case statement. Notice that the spaces after the instances of if were included inside the mbox declarations.f(n) = \begin{cases} n/2, & \mbox{if } n\mbox{ is even} \\ 3n+1, & \mbox{if } n\mbox{ is odd} \end{cases}
.
Simultaneous Equations
Here we have a very simple application of the case statement.\begin{cases} 3x + 5y + z \\ 7x – 2y + 4z \\ -6x + 3y + 2z \end{cases}
.
Matrices
Matrices can be assembled by using the array statement, like in this example:\left| \begin{array}{cc} x_{11} & x_{12} \\ x_{21} & x_{22} \end{array} \right|
Matrix frames are provided by \left and \right. If you suppress these statements, it will be displayed like:
\begin{array}{cc} A & B \\ C & D \end{array}
However, there is another statement, the matrix declaration, slightly easier to use:
\begin{matrix} x & y \\ z & v \end{matrix}
The frames of the matrix can be displayed in several forms, by just changing the matrix declaration to vmatrix, Vmatrix, bmatrix, Bmatrix or pmatrix, as shown ahead:
\begin{vmatrix} x & y \\ z & v \end{vmatrix}
\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}
\begin{bmatrix} x & y \\ z & v \end{bmatrix}
\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}
\begin{pmatrix} x & y \\ z & v \end{pmatrix}
As a final example, let us construct more complicated matrices and matricial expressions:
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
Now, we will show a first matricial expression:
\left[ \begin{array}{c} x_1 \\ x_2 \end{array} \right] = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \times \left[ \begin{array}{c} y_1 \\ y_2 \end{array} \right]
and, here is another example, now using two kinds of vectors:
\begin{bmatrix} xz & xw \\ yz & yw \end{bmatrix} = \left[ \begin{array}{c} x \\ y \end{array} \right] \times \left[ \begin{array}{cc} z & w \end{array} \right]
No comments:
Post a Comment
Thank you