Matrix multiplication and composition of linear
... 1. There exists an n × p matrix B such that T = TB , i.e., such that T (X) = TB (X) for all X ∈ Rp . 2. T satisfies the principle(s) of superposition: (a) T (X + X 0 ) = T (X) + T (X 0 ) for all X and X 0 in Rp , and (b) T (cX) = cT (X) for all X ∈ Rp and c ∈ R. Proof: The proof that (1) implies (2) ...
... 1. There exists an n × p matrix B such that T = TB , i.e., such that T (X) = TB (X) for all X ∈ Rp . 2. T satisfies the principle(s) of superposition: (a) T (X + X 0 ) = T (X) + T (X 0 ) for all X and X 0 in Rp , and (b) T (cX) = cT (X) for all X ∈ Rp and c ∈ R. Proof: The proof that (1) implies (2) ...
2-23-2005
... • Many physical quantities such as temperature and speed are measured with a single number. But other quantities require more than one number. Examples include velocity (which=speed + direction) and certain forces where the strength and the direction are important. • Vectors can be looked both algeb ...
... • Many physical quantities such as temperature and speed are measured with a single number. But other quantities require more than one number. Examples include velocity (which=speed + direction) and certain forces where the strength and the direction are important. • Vectors can be looked both algeb ...
Quantum Mechanics Problem Sheet 5 Basics 1. More commutation
... Basics 1. More commutation relations involving the angular momentum. Remember that both R̂ and L̂ are vectors, i.e. each of them is a triplet of operators. 2. More about the Hamiltonian in spherical coordinates. Useful for practice. 3. There are two aspects to this problem: i) you are looking for bo ...
... Basics 1. More commutation relations involving the angular momentum. Remember that both R̂ and L̂ are vectors, i.e. each of them is a triplet of operators. 2. More about the Hamiltonian in spherical coordinates. Useful for practice. 3. There are two aspects to this problem: i) you are looking for bo ...
