A linear system consists of two or more equations involving the same variables. A solution is an assignment of values that satisfies all equations simultaneously. Linear systems are fundamental in modern mathematics and engineering
Determinant is a scalar value from matrix operations. Can be denoted in three ways: determinant, determinant of matrix, determinant of matrix element
Matrix-vector product requires equal number of columns in matrix and rows in vector. Product is calculated by dot product of vector with each row of matrix. For single-row matrix, product is just dot product
Inverse of matrix A (A-1) is matrix where AA-1 = A-1A = I. Matrix is invertible only if determinant is non-zero. Matrix has no inverse if determinant is zero
Matrix is a rectangular array of numbers arranged in rows and columns. Matrix dimensions are denoted as m × n. Elements are denoted by variables with two subscripts
NumPy's linalg.inv() computes the multiplicative inverse of a matrix. The inverse matrix multiplies with the original matrix to form an identity matrix. The function requires a square matrix as input parameter