"The laws of logic are immaterial, universal, and invariant; they're unchanging."
"Invariance means that the notion of a dog shouldn't matter if that dog is translated in the image or rotated or scaled."
"If you have a field that has that kind of invariance, that it is a complex number but it doesn't matter how we choose to define what is the real part and what is the imaginary part, then you have a symmetry."
"Symmetry is a way of saying that there's a transformation we can do to some object that leaves its essential features invariant."
"Every zero eigenvalue corresponds to some kind of invariance in your system."
"There must be something invariant, something which doesn't vary if it is translated from one language to the other language."
"The Conservation of Energy means a certain magic combination connected to the velocity of the object and to its location, U depends on x, that does not change with time."
"The space-time interval is invariant for all observers in special relativity."
"A mathematical object that measures or models dependence should be invariant under strictly increasing transformations of the margins."
"The invariance principle is an extremely important result."
"Reference frames essentially allow us to create a single invariant structure that completely describes an object or a concept."
"Most things are relative. Distance between events -- relative. Time interval between events -- relative. But this combination is somehow invariant. Everybody agrees on what it is."
"Tensors are objects that are invariant under a change of coordinates, and have components that change in some special predictable way under a change of coordinates."
"Adding extra matter on the outside doesn't change anything at all."
"Point sets should be invariant under transformations."
"The Lorentz invariant inner product of two vectors is something which will not change when you do Lorentz transformation."
"The dot product is an invariant. This is a very important notion."
"Being invariant to the choice of parameterization seems like a good thing."
"The relationship between the mouth and the face is something that's completely invariant; that doesn't depend on viewpoint."
"The relationship between parts and wholes, that's what's invariant, at least for rigid objects."
"The invariance of wave equations follows if the equation has the form that some scalar is equal to zero."
"This equation has the virtue of being the same in every reference frame."
"The result of the integral will always be the same, no matter if we're using Cartesian coordinates or polar coordinates or whatever else we choose."
"The laws of physics are invariant under rotations, but this room isn't."
"A topological invariant is something which is not changed under small deformations."
"The Hall conductivity is also serving as a topological invariant."
"The vector field del F is invariant; the geometric vectors are always the same and don't depend on the coordinate system."
"Symmetries are operations that you can do on states of systems that don't change the equations."
"The laws of physics are invariant in any individual frame of reference."
"For a field to satisfy a gauge theory, it must be invariant to changes in the underlying field which vary in some way from place to place or from time to time."
"The electromagnetic field tensor, and the important thing about it is that it's gauge invariant."
"The coefficient of variation stays the same when we multiply every observation by three or by anything."
"Tensors are mathematical tools that are important for studying relativity because they help us write the laws of physics in a way that's the same in all coordinate systems."
"Total curvature is a topological invariant of a surface."
"Minkowski vectors, also called four vectors, are vectors in space-time that all inertial observers agree on."
"The four velocity vector big U is invariant in all coordinate systems."
"The Minkowski length of all four velocity vectors is c, the speed of light in a vacuum."
"Symmetries are operations that you can do on a system which don't change the description, which don't change the phenomena, which don't change the energy levels."
"It's really useful for studying and processing surfaces because it's isometry invariant."
"The Laplacian is invariant to rigid motions and to isometries."
"Adding a constant to each value of a one variable data set changes the mean but not the standard deviation."
"Reflections and rotations are going to preserve distance and angles."
"An eigenvector... does not change direction; it may change lengths but it won't change direction."
"Since the surface is invariant by assumption, the volume of all those points inside will also be invariant."
"The solid torus is an invariant object, surface plus interior, as well as that the surface is invariant also."
"We require that the scalar field should be invariant under a local gauge transformation."
"A reflection, a rotation, or a translation always preserve distance and angle measure; they never change the size of the shape."
"A rigid motion is any transformation that does not change the size nor the shape of an object."
"Symmetry is a transformation that maps a figure onto itself."
"The covariant derivative of a four-vector is the same in all coordinate systems, even if different coordinate systems will disagree on its components."
"The only quantity that all inertial frames seem to agree on is the speed of light in a vacuum, c."
"The space-time invariant s squared is the same in all orthonormal space-time coordinate systems."
"The laws of physics are invariant in inertial frames of reference."
"Symmetric states are quantum states that don't change at all when you exchange two particles."
"Some of these properties are invariant to geometrical transformation like translation, rotation, scaling."
"The idea is that this combination of a detector and the way that the SIFT descriptor works is kind of invariant to these kinds of scale and rotation and even some perspective change issues."
"The moment of a force at a given point is invariant under the operation of sliding the force along the line of action."
"If k is equal to one, there's no change in length."
"The physical structures of the universe are variable, but the speed of light is not."
"A good learning system should develop internal representations for those objects that are invariant to the transformations possible."
"Jeffrey's priors satisfy reparameterization; they're invariant by transformation of your parameter."
"The rank of a matrix is not affected if I multiply it with invertible matrices."
"The discriminant of a polynomial is invariant under the action of SL2."
"The statistics of pixels is the same anywhere on an image; images are translation invariant."