If a is the scale factor – the current distance between any two points in space- then the rate of change of that scale factor in relation to the size of the universe is given as : Where is derived from a…
read moreA Vector Space is a set of vectors that may be added together and scaled. When we say they may be scaled, we mean that they may be multiplied by numbers called scalars. For example, we may multiply all of the vectors…
read moreRicci calculus describes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold. It is another name for absolute differential calculus, which is the foundation of tensor calculus. The Ricci Curvature Tensor is a fundamental component…
read moreLinear algebra, or Modern Algebra, is algebra with vector values – i.e. more than one parameter – in place of scalar values like numbers, which have a single scalar parameter. Linear means we can add and scale vectors.
read moreEinstein Summation Notation is a notational convention that implies summation over a set of indexed terms in a formula. It is simply meant as a shortcut in the writing of formulas. It is primarily used in the application of linear algebra to…
read moreThe Metric Tensor in General Relativity is a Set of 10 parameters ascribed to each point in space, the values of which describe the geometry of spacetime. Metric means “measure,” and a tensor is simply the higher dimensional analogue of vector, i.e….
read moreA Radian is a unit of angle measure, equal to an angle at the center of a circle whose arc length is equal to the radius length. In a unit circle, whose radius is 1, 360 degrees is equal to 2π radians…
read moreA unit circle is simply a circle of radius 1. 1 what? 1 anything. The most important thing is that if we choose a radius of “1,” it makes it easy to understand the circumference of the circle. The circumference of a…
read moreA derivative is the instantaneous rate of a change of a variable with respect to another variable. For example, Velocity is the rate of change – or derivative – of an object with respect to time. When we say a plane is…
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