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1. Presented To
MD. Mehedi Hasan

2. • Introduction Of Matrix
• Diagonal and triangular matrix
• Identity matrix
• Symmetric or skew-symmetric matrix
• Invertible matrix and its inverse
• Definite matrix
• Orthogonal matrix
Content Layout

3. Presented by
NAME ID
PRANTO DAS 161-15-7609
APURBO DATTA 161-15-7610
SREE SHOPON KUMAR 161-15-7598
RUBEL BISWAS 161-15-7668
HELAL SHEAK 161-15-6771

4. IntroductIon of MatrIx

5. If all entries of A below the main diagonal are zero, A is called an upper triangular matrix.
U =
Similarly if all entries of A above the main diagonal are zero, A is called a lower triangular matrix.
If all off-diagonal elements are zero, A is called a diagonal matrix.
dIagonal and trIangular MatrIx

6. The identity matrix In
of size n is the n-by-n matrix in
which all the elements on the main diagonal are equal to 1 and all other elements are equal to 0.
AIn
= Im
A = A for any m-by-n matrix A.
IdentIty MatrIx

7. A square matrix A that is equal to its transpose,
that is,
A = AT
,
is a symmetric matrix.
If instead, A is equal to the negative of its transpose,
that is,
A = −AT
,
then A is a skew-symmetric matrix.
Symmetric or Skew-Symmetric matrix

8. A square matrix A is called invertible or non-singular if there exists a matrix B such that
AB = BA = In
If B exists, it is unique and is called the inverse matrix of A, denoted A−1
.
invertible matrix and itS inverSe

9. A symmetric n×n-matrix is called positive-definite, if for all nonzero vectors
x R∈ n
the associated quadratic form given by
Q(x) = xT
Ax
Allowing as input two different vectors instead yields the bilinear form associated
to A:
BA (x, y) = xT
Ay
definite matrix

10. An orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal
unit vectors.
Equivalently, a matrix A is orthogonal if its transpose is equal to its inverse:
A T
= A − 1
which entails
AT
A = AAT
= In
where I is the identity matrix of size n
OrthOgOnal matrix