Prove change of basis does not change trace? Why biharmonic need two boundary conditions? Define with example. Scalar What does it mean for a function to be orthogonal? Find constraint equations (if any) that b must satisfy in order for Ax = b to be consistent. ...
Find an ordered basis BB of C3[x]C3[x], such that [p]B= ⎜⎜⎜100i⎞⎠⎟⎟⎟[p]B=(100i) for the polynomial p=2+2x+2x2+2x3p=2+2x+2x2+2x3. The notation I'm struggling with is [p]B[p]B. What does that mean? I've also seen notations like [p]BJ...
What does that mean numerically? Any matrix that you represent in floating point numbers is actually a representative of a whole bunch of matrices. Each entry is only known up to a certain precision. But this bunch of matrices does contain some matrix which is diagonalizable! This is exactly,...
skills of local designers and workers also formed the basis of an important shipbuilding industry. But the big profits were to be made on trade with faraway places. And since sea captains often 10became part owners of their ships, they had a strong interest in the commercial success of their...
The vector x is in the subspace H with a basis B = {b1, b2}. Find the B-coordinate vector of x. b1 = 1 4 -2 b2 = -2 -7 3 x = -1 -2 0 [x]B = ? What does it mean for a vector to span a space? How to prove something is a vector space? How to prove that some...
This is just elementary linear algebra. Now, if we hold y constant and vary x, how much does x′ vary? In other words, what is the partial derivative of x′ with respect to x? This is denoted by ∂x′/∂x, and clearly we have ∂x′/∂x = cos(θ). Now we ask a ...
NLP (Text) Imbalanced Learning Intro to Time Series Intro to Algorithms Linear Algebra LSTMsLong Short-Term Memory Networks OpenCV Optimization Probability Python (scikit-learn) Python for Machine Learning R (caret) Stable Diffusion Statistics Weka (no code) XGBoost...
It is natural to ask whether the Fefferman-Stein decomposition (1) can be made linear in , in the sense that each of the depend linearly on . Strictly speaking this is easily accomplished using the axiom of choice: take a Hamel basis of , choose a decomposition (1) for each element of...
The whole argument rested on a basis of conjecture Basis The most important or necessary part of something; The basis of this drink is orange juice Common Curiosities How does the meaning of "bases" differ in general usage? "Bases" is the plural of "base," referring to multiple foundations...
(uncountable) A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method. Logic The study of the principles and criteria of valid inference and demonstration. Logic ...