"An orthonormal collection of vectors forms a basis for the vector space."
"Persistence is based upon definite causes."
"The Rustic Harrow they're using is based on one depicted in a period illustration."
"The Number 4 formed the foundation of that."
"It's all based on emotion, right? Yeah, and how it makes you feel."
"It's not always necessary to use a grid, but they can be very beneficial as a basis for your design."
"Artistry has been the basis of maturity."
"Love comes first and it's the basis for power."
"All this stuff is based on seniority."
"Freedom of speech, give me a break. You've got to, that's the basis of everything."
"There's no predicate for it. There's no basis for it."
"...there is really no real basis for what we've done except tradition."
"There's no basis for the law of non-contradiction apart from the word of God."
"The four elements are the basis of our world, of our realm, of our reality."
"The central difference is that in Christ and his death and resurrection, I find an adequate basis for forgiveness."
"Basic human nature is more compassionate, that's the basis."
"The system model becomes a basis of communication at a system level."
"The second part says that there exists a basis of RN which consists of eigenvectors of a."
"When we make decisions, we have some basis for making them."
"The eigenstates of a Hermitian operator form a basis in state space, which is crucial for predicting the outcome of a measurement in quantum mechanics."
"The inside basis is the partnership's basis in the assets it receives from the partners."
"The only thing that you really need to consider yourself is how large a basis are we going to use."
"It's like a foundation to a house."
"A plus iB can be taken to be the natural basis elements."
"The output of the volume form is always 1 for orthonormal basis vectors."
"A basis of a vector space V is a linearly independent set which spans V."
"If we want to try to find a basis for a vector space, we first need to find a set of vectors which span the whole vector space."
"The dimension of the vector space means the number of elements in the basis."
"It's got to be based on what's true, what's factual."
"A foundation is the basis for something to exist."
"They span R3, so they are a basis for R3."
"If a set of vectors spans a subspace and is linearly independent, then it is a basis for that subspace."
"Every disease state has a biochemical basis."
"You can always reconstruct a tensor from its components and the corresponding basis."
"The basis can be thought of as the building blocks which together make up all of the elements of a particular space."
"The dimension of the subspace is the number of elements in the basis."
"It's a foundation for almost everything else."
"There is always a scientific basis in folklore."
"The Fourier transform is really just a linear map from one basis to another."
"The eigenvectors form a complete basis that spans RN if the eigenvalues of Lambda are real and distinct."
"We've identified a basis which is a vector in the vector space, and we've identified the components of this vector."
"Quantum physics says the basis of the world is non-material."
"A basis is a set of generators for the space of vectors."
"The transformation is uniquely determined once we know what it does to each element of a basis."
"There is a rational basis through which you can adopt theism."