class_docstr: The multivariate normal distribution on `R^k`.
  
  The Multivariate Normal distribution is defined over `R^k` and parameterized
  by a (batch of) length-`k` `loc` vector (aka "mu") and a (batch of) `k x k`
  `scale` matrix; `covariance = scale @ scale.T`, where `@` denotes
  matrix-multiplication.
  
  #### Mathematical Details
  
  The probability density function (pdf) is,
  
  ```none
  pdf(x; loc, scale) = exp(-0.5 ||y||**2) / Z,
  y = inv(scale) @ (x - loc),
  Z = (2 pi)**(0.5 k) |det(scale)|,
  ```
  
  where:
  
  * `loc` is a vector in `R^k`,
  * `scale` is a linear operator in `R^{k x k}`, `cov = scale @ scale.T`,
  * `Z` denotes the normalization constant, and,
  * `||y||**2` denotes the squared Euclidean norm of `y`.
  
  The MultivariateNormal distribution is a member of the [location-scale
  family](https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
  constructed as,
  
  ```none
  X ~ MultivariateNormal(loc=0, scale=1)   # Identity scale, zero shift.
  Y = scale @ X + loc
  ```
  
  #### Examples
  
  ```python
  tfd = tfp.distributions
  
  # Initialize a single 3-variate Gaussian.
  mu = [1., 2, 3]
  cov = [[ 0.36,  0.12,  0.06],
         [ 0.12,  0.29, -0.13],
         [ 0.06, -0.13,  0.26]]
  scale = tf.linalg.cholesky(cov)
  # ==> [[ 0.6,  0. ,  0. ],
  #      [ 0.2,  0.5,  0. ],
  #      [ 0.1, -0.3,  0.4]])
  
  mvn = tfd.MultivariateNormalLinearOperator(
      loc=mu,
      scale=tf.linalg.LinearOperatorLowerTriangular(scale))
  
  # Covariance agrees with cholesky(cov) parameterization.
  mvn.covariance()
  # ==> [[ 0.36,  0.12,  0.06],
  #      [ 0.12,  0.29, -0.13],
  #      [ 0.06, -0.13,  0.26]]
  
  # Compute the pdf of an`R^3` observation; return a scalar.
  mvn.prob([-1., 0, 1])  # shape: []
  
  # Initialize a 2-batch of 3-variate Gaussians.
  mu = [[1., 2, 3],
        [11, 22, 33]]              # shape: [2, 3]
  scale_diag = [[1., 2, 3],
                [0.5, 1, 1.5]]     # shape: [2, 3]
  
  mvn = tfd.MultivariateNormalLinearOperator(
      loc=mu,
      scale=tf.linalg.LinearOperatorDiag(scale_diag))
  
  # Compute the pdf of two `R^3` observations; return a length-2 vector.
  x = [[-0.9, 0, 0.1],
       [-10, 0, 9]]     # shape: [2, 3]
  mvn.prob(x)    # shape: [2]
  ```
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code: def _default_event_space_bijector(self):
      return identity_bijector.Identity(
          validate_args=self.validate_args
      )
  
imports: import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import identity
  from tensorflow_probability.python.bijectors import scale_matvec_linear_operator
  from tensorflow_probability.python.bijectors import shift
  from tensorflow_probability.python.distributions import kullback_leibler
  from tensorflow_probability.python.distributions import normal
  from tensorflow_probability.python.distributions import sample
  from tensorflow_probability.python.distributions import transformed_distribution
  from tensorflow_probability.python.internal import distribution_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow_probability.python.internal import tensorshape_util
label_desc: Use image node_id 12 for calling the MultivariateNormalLinearOperator obj's underlying member method code with example usage: obj._default_event_space_bijector() and returns: identity_bijector