LCD (Liquid crystal display) Television:

Passive matrix addressing:

Passive matrix addressing is an addressing scheme used in earlier LCD displays, and may be used in future LCD displays. This is a matrix addressing scheme meaning that only m + n control signals are required to address a m × n display. A pixel in a passive matrix must maintain its state without active driving circuitry until it can be refreshed again.

A new display technology uses a bi-stable pixel, which maintains its state indefinitely without the need for individual transistor elements at each pixel.

The signal is divided into a row or select signal and a column or video signal. The select voltage determines the row that is being addressed and all m pixels on a row are addressed simultaneously. When pixels on a row are being addressed, a V_sel potential is applied, and all other rows are unselected with a V_unsel potential. The video signal or column potential is then applied with a potential for each m columns individually. An on-lighted pixel corresponds to a V_on, an off-switched corresponds to a V_off potential.

The potential across pixel at selected row i and column j is

V_ij = V_sel − V_{on | off}

and

V_ij = V_unsel − V_{on | off}

for the unselected rows.

Theres also the Active matrix addressing, if you are intrested in some more information about it visit : http://en.wikipedia.org/wiki/Active_matrix_addressing .

Since a 2 x 2 matrix corresponds uniquely to a linear transformation from R² to R², we can think of a matrix as transforming a planar figure into a new planar figure.

Example

Consider the matrix

and the triangle with vertices (0,0), (12), (5,3). We have

It is a property of linear transformations that if the matrix is nonsingular, then line segments map onto line segments. Hence triangles map onto triangles. The picture below shows the original triangle.

---

Some Basic Transformations

There are certain basic transformation that are building blocks for general transformations.

Example Reflection With Respect to the x axis.

To find the matrix for this transformation, we consider where the vectors e₁ and e₂ are mapped. The reflection with respect to the x-axis makes the y-coordinate negative and leaves the x-coordinate constant. We have

L(1, 0) = (1, 0) L(0, 1) = (0, -1)

These vectors are the column vectors for the matrix. We have

---

Example Reflection About the Line y = x

We see that

L(1,0) = (0,1) L(0,1) = (1,0)

so that

---

Example Rotation About an Angle q

The point (0,1) rotated about this angle is on the unit circle at radian angle q. The point (1,0) rotated about this angle is on the unit circle at radian angle p/2 + q. We have

L(1,0) = (cos q, sin q) L(0,1) = (cos(p/2 + q), sin(p/2 + q) = (-sin q, cos q)

We have

---

Example Shear in the y-direction

Another transformation that is common in computer graphics is a shear in the x or y direction. The picture below gives and example

The matrix that makes this happen is

for some constant k.