Sustainable Energy

In Oxford dictionary sustainable means “able to be maintained at a certain rate or level.”  According to the United Nations sustainability is defined as “meeting the needs of the present without compromising the ability of future generations to meet their own needs .” The important question to ask is why we are discussing sustainable energy, and the answer is either we have limited sources of energy or we are polluting our environment at the incredibly fast rate. In fact, we are facing both of these challenges, but at the consumer level, we don’t realize these.

The major sources of energy are coal, oil and natural gas. Two major problems with these resources are they are: 1) limited and are getting depleted; this means that our future generations will face energy scarcity. 2) Coal, the main energy source emit lots of carbon dioxide, a green house gas which eventually results in the greenhouse effect. The greenhouse effect deals with heating of our climate which eventually melts the glaciers raises water levels and affects global ecosystem badly.

Sustainable energy aims to find solutions to our existing energy problem by proposing renewable energy sources which regenerate naturally and produce clean energy. These sources include solar, wind, water, biogas, geothermal energy. All these sources are inexhaustible. Sustainable energy also includes the practices of energy efficiency and conservation.

Stephen Pacala, an environment biologist at Princeton University mentions that we can handle the increasing carbon dioxide challenge with following four options:

1. Efficiency: Develop technologies or appliances which are energy efficient
2. Tripling our nuclear power plants
3. Cleaning coal plants by burying carbon emissions
4. Harnessing SUN’s energy using solar panels etc.

Eigen vectors and Eigen values

A point x in a two-dimensional space represents a vector because it has a magnitude and a direction with respect to the center (0, 0). A scalar multiplication of x represents another vector which lies on the same line (elongated or scaled down) as that of vector x.  When we multiply vector x with a matrix A, it again results in a vector but now the resultant vector will be either in the same previous direction as that of x or in a new direction. Also, the resultant vector will get either scaled up or down. If the resultant vector lies in the same direction then we say vector x is Eigen vector of matrix A, otherwise, it is not an Eigen vector. A 96 seconds youtube video explains the same concept visually.

Corresponding to Eigen vector, we too get a scalar value ($\lambda$) which on multiplying vector x results in the same vector as that obtained by above matrix multiplication. Mathematically,

$A*x = \lambda*x$

Here, $x$ refers to Eigen Vector and $\lambda$ refers  to Eigen value.

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