The diagonal form - If an nxn matrix has n independent eigenvectors, then the matrix has a diagonal form, where the main diagonal contains the eigenvalues, and all other elements are zero.Characteristic equation - The solutions to the characteristic equation will be the eigenvalues.Eigenvalue - An eigenvalue of an nxn matrix A is a number, where there is a non-zero vector such that A multiplied by the vector is equal to the number multiplied by the vector.Eigenvector - An eigenvector of an nxn matrix A is a non-zero vector, where there is a real number such that A multiplied by the vector is equal to the number multiplied by the vector.There are those whose determinant is zero, and there are those whose is non-zero. Singular and invertible matrices - The nxn matrices can be classified into two large groups.The expansion rule - The essence of the expansion rule is that for an nxn matrix of any size, the rather nasty calculation of its determinant can be reduced to calculating the determinants of 2x2 matrices, which is fairly easy.Sarrus' Rule - There is a rule for calculating the determinant of a 3x3 matrix.Definition of determinant - The determinant takes a matrix, and turns it into a single number. The equation of the plane - Here we will develop the equation of a plane.The equation of the line - We will develop the various forms for the equation of lines in plane and three dimensional space.Angle between the two vectors - To calculate the angle between the two vectors, we write their dot product using two formulas.Dyadic product - The dyadic product, is an algebraic operation that takes two vectors and turns into a matrix.Cross product - The cross product, is an algebraic operation that takes two vectors and turns into anather vector.Dot product - The dot product, or sometimes inner product, is an algebraic operation that takes two vectors and turns into a single number.Transpose - The transpose matrix is created by swapping the rows and the columns of the matrix.Square and diagonal matrices - It is a square-shaped matrix with the same number of rows and columns.The diagonal matrix is a square matrix where all elements outside the main diagonal are zero.Matrix operations - Scalar multiplication, addition and multiplication.An nXk matrix is simply a rectangular array of numbers, arranged in n rows and k columns. Matrices - Matrices are really harmless creatures in mathematics.
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