Micromaser
Micromaser

Other Approaches to 102 Linear algebra, Groups and polynomials
Other Approaches to 102 Linear algebra, Groups and polynomials

3. Lie derivatives and Lie groups
3. Lie derivatives and Lie groups

ENGO Assessment of Environmental Goal Achievement under
ENGO Assessment of Environmental Goal Achievement under

chapt12_lecture_updated
chapt12_lecture_updated

determinants
determinants

... The second technique uses row operations on A to obtain an upper triangular matrix while we keep track of how the row operations used effect the value of the determinant. ...
Hilbert spaces and the projection theorem 1 Vector spaces
Hilbert spaces and the projection theorem 1 Vector spaces

4 Singular Value Decomposition (SVD)
4 Singular Value Decomposition (SVD)

Solutions
Solutions

Lecture 28: Similar matrices and Jordan form
Lecture 28: Similar matrices and Jordan form

Time reversal (reversal of motion)
Time reversal (reversal of motion)

Einstein`s E mc2
Einstein`s E mc2

Chapter 3
Chapter 3

classical theoretical physics II
classical theoretical physics II

Linear Transformations and Group
Linear Transformations and Group

[2015 solutions]
[2015 solutions]

Additional notes
Additional notes

Commutative Law for the Multiplication of Matrices
Commutative Law for the Multiplication of Matrices

... from left to right in actually operating with the commutativity as it is a scalar. This interpretation is ambiguous in meaning, although we can consider that the column vectors of the product UΛ are λ1 u1 , λ2 u2 , . . . , λn un . From a pedagogical standpoint, it is not necessarily easy for some st ...
1 Basis
1 Basis

Vector Spaces, Affine Spaces, and Metric Spaces
Vector Spaces, Affine Spaces, and Metric Spaces

Figure 4-5. BLOSUM62 scoring matrix
Figure 4-5. BLOSUM62 scoring matrix

Plan of Lectures - The Budker Group
Plan of Lectures - The Budker Group

Systems of Linear Equations
Systems of Linear Equations

Document
Document

Two, Three and Four-Dimensional
Two, Three and Four-Dimensional

Four-vector

In the theory of relativity, a four-vector or 4-vector is a vector in Minkowski space, a four-dimensional real vector space. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations, boosts (a change by a constant velocity to another inertial reference frame), and temporal and spatial inversions. Regarded as a homogeneous space, the transformation group of Minkowski space is the Poincaré group, which adds to the Lorentz group the group of translations. The Lorentz group may be represented by 4×4 matrices.The article considers four-vectors in the context of special relativity. Although the concept of four-vectors also extends to general relativity, some of the results stated in this article require modification in general relativity.