Student reasoning about the invertible matrix theorem in linear algebra. ZDM Mathematics Education, 46, 389-406.Wawro, M. (2014, this issue). Student reasoning about the Invertible Matrix Theorem in linear algebra. ZDM—The International Journal on Mathematics Education . : 10.1007/s11858-014-...
Often, however, the modes of higher-order data sets have different physical meaning (for example, time vs. spatial coordinates). The new family of tensor–tensor products together with the recursive approach gives us an opportunity to tailor the products to suit the physical interpretations across...
Existence of such an algebra object is equivalent to the existence of a fiber functor for the fusion category. A fiber functor sends every object X to a vector space F (X) whose dimension is the quantum dimension of X, meaning that, as observed in Theorem 2 in [31], a necessary ...
Individual and collective analyses of the genesis of student reasoning regarding the invertible matrix theorem in linear algebra In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an in... MJ Wawro -...
you have to check that for an nxn matrix given by {v1v2v3 •••vn} with n vectors with n components, there are not constants (a, b, c, etc) not all zero such that av1 + bv2 + cv3 + ••• + kvn =0(meaning only the trivial ...
The fine details of this correspondence, including the precise algebraic meaning/analogue of collinearity, are furnished by employing the representation of GQ(2,â4) as a quadric in PG(5,â2) of projective index one. An interesting physics application of our findings is also ...
The fine details of this correspondence, including the precise algebraic meaning/analogue of collinearity, are furnished by employing the representation of GQ(2,4) as a quadric in PG(5,2) of projective index one. An interesting physics application of our findings is also mentioned....
MJOM Invertible and Isometric Weighted Page 11 of 14 173 Thus, equality must hold throughout, meaning that F +λF φ = F + F φ . Hence |(F + λF φ)(0)| + p(F + λF φ) = |F (0)| + p(F ) +|(F φ)(0)| + p(F φ) . Since p(F + λF φ) ≤ p(F ) ...
Any matrix that is its own inverse is called an involutory matrix (a term that derives from the term involution, meaning any function that is its own inverse). Invertible matrices have the following properties: 1. If M is invertible, then M−1 is also invertible, and (M−1)−1 ...